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On behalf of the International Programme Committee and the Local Organizing Committee we invite you to join the VII International Conference “Models in Quantum Field Theory” to be held in Saint Petersburg, Russia on October 10-14 of 2022.
MQFT is a biennially held international conference this year dedicated to the 82nd anniversary of professor Alexander Nikolaevich Vasiliev (1940-2006) and 80th anniversary of professor Vladimir Dmitrievich Lyakhovsky (1942-2020). From year to year, the conference attracts the most distinguished members of the world-famous centres for theoretical physics. The main topics of the conference are related to the most actual and important problems related to the construction and investigation of the quantum field theory models. During the conference, it is proposed to discuss the modern methods of QFT and applications of these methods to the elementary particle physics and statistical physics, gravitation and cosmology, mathematical problems and methods in quantum field theory, and integrable models.
During the conferences, the special importance is placed upon the methods and approaches created and developed by the researchers of “Vasiliev scientific school”, the school of theoretical physics that was established by Alexander Nikolaevich Vasiliev and has since then aquired an international scope. Currently, as many as 10 professors and 20 Ph.D. researchers belong to the school. Their successful work in the field of theoretical physics is conducted either in Russia or around the world, many of them have developed their own methods and approaches and acquired many students of their own. Results obtained by A.N.Vasiliev and his followers revealed the deep intrinsic affinity between classical complex systems with many degrees of freedom and quantum objects, which allowed to apply successfully the powerful mathematical methods of the quantum field theory to the phenomena of seemingly completely different nature.
This year the conference will include an extended section on the mathematical foundations of quantum field theory that is dedicated to the 80th anniversary of professor Vladimir Dmitrievich Lyakhovsky (1942-2020), who was a close friend of Alexander Nikolaevich Vasiliev and the organizer of the first MQFT conferences. In this section we welcome contributions that are related to the scientific interests of Vladimir Dmitrievich: representation theory, symmetries in QFT, quantum integrable systems, quantum groups.
The conference is accompanied by III International Workshop “Lattice and Functional Techniques for QCD.”
The conference hall is located on the Aptekarsky island in the historical center of Saint Petersburg, arguably the most beautiful Russian city and a cultural capital of Russia. Saint Petersburg is the home of the Hermitage, one of the largest art museums in the world, and to the Mariinsky Theatre which resident ballet company is one of the most famous in the world. The fine European architecture of the city is best enjoyed from abroad one of the many tourist boats that roam numerous rivers and man-made channels. The drawing of the bridges during the night-time is particularly lovely, even during late August when the famous season of white nights is over.
The Aptekarsky island is separated from Petrogradsky Island by the Karpovka River, from Kamenny Island and Krestovsky Island by the Malaya Nevka. It is home to Saint Petersburg Botanical Garden, which is the first botanical garden in Russia.
Russian and English are official languages of the conference but we ask participants to use only English in their slides. Posters can be in either Russian or English.
We hope that you will be able to attend and contribute to the success of the meeting.
We look forward to seeing you in Saint Petersburg, Russia in October 2022.
A review of the achievements in the theoretical study of (magneto)hydrodynamic turbulence by the methods of quantum field theory is presented. The main focus is given to the problem of justification of the Kolmogorov scaling and its violation, the calculation of critical exponents determining the scaling behavior of the statistical correlations of the studied random fields (velocity, magnetic field, concentration) in the inertial interval of space scales, the calculation of representative parameters such as the Kolmogorov constant, skewness factor, Prandtl number, etc.
D.I.Kazakov (JINR)
RG Equations in Non-renormalizable Theories
We construct the RG equations for the scattering amplitudes and effective potential
In a a set of non-renormalizable theories. We show that they are a consequence of locality
rather than multiplicative renormalizability. These RG equations sum up the leading log terms
in all orders of PT and allow one to explore the high energy/field behaviour.
We consider correlation functions for Poincare and de Sitter invariant states in the corresponding spaces. We study loop corrections to these correlation functions in various charts of these spaces. We find that the correcations contain certain IR contributions which affect the properties of the correlation functions and in certian cases can lead to the violation of the isometry in the loops.
We discusses the efficient quantum-quasiclassical method developed by V.S. Melezhik with co-authors [1-4], which has been successfully applied to calculate various few-body processes and has made it possible to resolve a number of topical problems in atomic [1,3-5], mesoatomic [2], and nuclear physics [6]. In this approach, a few-body quantum problem is reduced to the simultaneous integration of a system of coupled quantum and classical equations: the time-dependent Schrödinger equation, which describes the quantum dynamics of slow light particles, and the classical Hamilton equations, describing the fast variables of heavy particles.
Recently [5], the approach was extended and adapted for quantitative description of pair collisions of light slow Li atoms with heavy Yb+ ions in the confined geometry of the hybrid atom-ion trap. On the basis of these calculations, a new method for sympathetic cooling of ions in a RF Paul trap was proposed. This approach also made it possible to perform calculations of the breakup cross sections into the low-energy region (up to 10 MeV/nucleon), in inaccessible so far to other methods, for the 11Be breakup on a heavy target [6].
The main focus in the report will be made on our recent analysis within the frame of this approach of the coupling between the center-of-mass (CM) and electronic motions in a 6D hydrogen atom, which arises in strong laser fields due to relativistic effects. In this case, the CM dynamics is treated classically, while the electronic motion is treated quantumly. So, in this approach it is naturally to investigate the idea proposed in the work [7] to use the CM-velocity spectroscopy (classical set up) for detecting the internal electron quantum dynamics.
The reported work was partly supported by the Russian Science Foundation, project no. 20-11-20257.
We build a systematic calculational method for the covariant expansion of the two-point heat kernel $\hat K(\tau|x,x')$ for generic minimal and non-minimal differential operators of any order. This is the expansion in powers of dimensional background field objects -- the coefficients of the operator and the corresponding spacetime and vector bundle curvatures, suitable in renormalization and effective field theory applications. For minimal operators whose principal symbol is given by an arbitrary power of the covariant Laplacian $(-\Delta)^M$, $M>1$, this result generalizes the well-known Schwinger--DeWitt (or Seeley--Gilkey) expansion to the infinite series of positive and negative fractional powers of the proper time $\tau^{1/M}$, weighted by the generalized exponential functions of the dimensionless argument $-\sigma(x,x')/2\tau^{1/M}$ depending on the Synge world function $\sigma(x,x')$. The coefficients of this series are determined by the chain of auxiliary differential operators acting on the two-point parallel transport tensor, which in their turn follows from the solution of special recursive equations. The derivation of these operators and their recursive equations are based on the covariant Fourier transform in curved spacetime. The series of negative fractional powers of $\tau$ vanishes in the coincidence limit $x'=x$, which makes the proposed method consistent with the heat kernel theory of Seeley--Gilkey and generalizes it beyond the heat kernel diagonal in the form of the asymptotic expansion in the domain $\sigma(x,x')\ll\tau^{1/M}$, $\tau\to 0$. Consistency of the method is also checked by verification of known results for the minimal second-order operators and their extension to the generic fourth-order operator.
We discuss thermalization process in the kinetic approximation in the presence of non--zero initial anomalous quantum expectation values on top of an initial non--plankian (non--thermal) level population. Namely we derive a system of ``kinetic'' equations for the level population and anomalous expectation values in four--dimensional massive scalar field theory with $\varphi^4$ self--interaction. We show analytically in the linear approximation that for small initial anomalous quantum average it relaxes down to zero. We show analytically that this system does not have an equilibrium solution with non--zero time independent anomalous expectation value.
In this paper we consider an initial state, containing non--plankian (non--thermal) level population, which is expressed via $Tr[\overset{\wedge}{\rho}a^+_{q}a_{q'}] \equiv $, and anomalous averages, $Tr[\overset{\wedge}{\rho}a_{q}a_{q'}]\equiv
To show this phenomenon we derive a system of kinetic equations for the level--population and anomalous average. Then we show that this system has a solution with zero anomalous average and plankian level--population only for such modes, which diagonalize the free Hamiltonian. To derive the system of the generalized kinetic equations we use the standard text book methods. To have an analytic headway we consider spatially homogeneous states and small initial anomalous averages. But we also derive the system of kinetic equations for $n_p$ and $\chi_p$ without the latter assumptions.
A review of the nonrelativistic quantum electrodynamics (NRQED) as applied to the bound state problem is given. The main corrections to nonrelativistic binding energies are derived, such as the relativistic Breit-Pauli Hamiltonian of the leading order ($m\alpha^4$), the radiative corrections of the leading order ($m\alpha^5$). Then it is shown how complex particles (hadrons) can be incorporated in the low-energy QED theory. We consider how higher-order corrections in the fine structure constant $\alpha$, including contributions of the order $m\alpha^7$, can be obtained and calculated from the NRQED formalism.
We investigate soliton collisions a one-parameter family of scalar field theories in 1+1D. The models have a sextic potential with three local minima, and for suitably small values of the parameter its kinks have an internal structure in the form of two weakly-bound subkinks. We show that for these values of the parameter kink collisions are best understood as an independent sequence of collisions of these subkinks, and that a static mode analysis is not enough to explain resonant structures emerging in this model. We also emphasise the role of radiation and oscillon formation in the collision process.
The total cross section of the process $e^+e^- \to \Lambda\bar{\Lambda}$ is calculated within the energy range close to the mass of $\psi(3770)$ charmonium state. Two different contributions were considered: the $D$-meson loop and the three gluon charmonium annihilation one. Both of them contribute noticeably and in sum fairly reproduce the data. Large relative phase for these contributions are generated with respect to the pure electromagnetic mechanism. As a by product the fit for the electromagnetic form factor of $\Lambda$-hyperon is obtained for large momentum transferred region.
The Standard Model (SM) has been tested and confirmed by many experiments.
Nowadays, the focus has shifted beyond the SM by seeking
new particles and new interactions. No new particles were observed
directly at the Large Hadron Collider (LHC) at CERN.
However, there are indirect hints for new physics (NP).
Among them semileptonic B-meson decays via charged current
(branching fractions are of order $10^{-3}$),
and rare B-meson decays via flavor changing neutral current
(branching fractions are of order $10^{-6}$).
All deviations from experiments (the so-called B-anomalies) admit an
interpretation in terms of Lepton Flavor Universality Violation.
At present time, effective theories are reliable tools for attempts to explain
B-anomalies.
We are analyzing new physics in the semileptonic decays
$B \to D^{(\ast)}\tau \nu_\tau$,
$B_c^+ \rightarrow J/\psi \tau^+ \nu_{\tau}$
($b-c$ transition), and in the rare decays
$B \to K^{(\ast)} \mu^+\mu^-$, $B_s \to \phi\mu^+\mu^-$,
$B \to K^{(\ast)} +\nu\bar\nu$.
($b-s$ transition).
We extend the Standard Model
by taking into account right-handed vector (axial), left- and right-handed
(pseudo)scalar, and tensor current contributions.
The necessary transition form factors are calculated in the full kinematic
$q^2$ range by employing a covariant quark model developed by us.
We provide constraints on NP operators based on
measurements of the ratios of branching fractions
and consider the effects of these operators on physical observables in
different NP scenarios.
A confirmation of new physics contributions in these decays would
change our understanding of matter and trigger an intense program
of experimental and theoretical research.
In the report the elastic electron-trinucleon scattering in the relativistic impulse approximation is considered. The amplitudes for a trinucleon have been obtained by solving the relativistic generalization of the Faddeev equations with a multirank separable kernel of the nucleon-nucleon interactions. The static approximation and additional relativistic corrections for the trinucleon electromagnetic form factors have been calculated for the momentum transfer squared up to 50 fm^-2.
Magnetic skyrmions (MS) are topologically protected configurations of local magnetization, observed, e.g., in non-centrosymmetric magnets with Dzyaloshinskii-Moriya interaction. In thin films MS arrange to 2D skyrmion crystals (SkX) [1]. The twisted character of skyrmionic configurations complicates an analysis of elementary excitations in such systems. We develop a novel approach that allows the study of magnon dynamics in presence of the topologically nontrivial background [2]. This approach is based on a combination of semiclassical methods and stereographic projection representation of the local magnetization.
The equilibrium configuration of SkX is defined in terms of the function of complex variable. We show numerically that the stereographic function of SkX corresponds rather precisely to a simple sum of stereographic functions for solitary skyrmions. Allowing infinitesimal variation of the stereographic function, we find normal modes of fluctuations in harmonic approximation. We calculate excitation spectrum of SkX and show that the appearing bands can be classified in terms of deformation types of individual skyrmions: dilatation, elliptical deformations etc. The topological properties of magnon band structure, i.e. Berry curvature and Chern numbers are discussed.
References:
In this contribution an application of two techniques for resummation of asymptotic series namely Borel-Pade technique and Borel-Leroy technique with conformal mapping to the case of a model with multiple coupling constants will be discussed and the results of application of these methods to the $O(n)$-symmetric $\phi^{4}$ model with a real antisymmetric tensor order parameter will be presented.
The number of particles created in a resonant cavity is known to grow linearly at large evolution times [J. Math. Phys. 34, 2742 (1993)]. Employing the Schwinger-Keldysh diagrammatic technique, I show that nonlinear interactions generate nonzero quantum averages and enhance this number. For simplicity, I discuss a $\lambda \phi^4$ massless scalar field in a cavity with perfectly reflecting walls vibrating at twice the fundamental frequency of the cavity.
Quantum field perturbation theory is widely used in theoretical physics. This gives excellent results in weak interaction models (e.g. QED). Otherwise, a few known first terms of such a series are not enough and additional information is needed. This report is devoted to models of statistical physics and critical phenomena using the renormalization group (RG) approach.
Traditionally, critical behavior is described using RG methods in the formalism of some regular expansion, usually the $(4-\epsilon)$-expansion. It is known that these series for calculating critical exponents are asymptotic, and a resummation procedure is necessary to obtain an adequate numerical result. This requires additional information. Usually, the parameters of the asymptotic behavior of the considered series are determined using instanton analysis. This has led to the use of various forms of Borel transforms.
As an addition to the standard quantum field perturbation theory, another perturbative procedure was developed. In this approach, one can calculate the same Green’s functions, but in the form of an expansion in an additional non-physical parameter for an arbitrary coupling constant. The resulting series converge. The application of the proposed approach to stochastic models (from B to H in the standard classification) is discussed.
Anomaly inflow is a relation between anomalies in quantum field theory on a manifold and anomalies in effective theories on the boundary. Relevant examples of the anomalies are the parity anomaly (the η invariant) and the global chiral anomaly (the Index of a Dirac operator). We study the η-invariant of a Dirac operator on a manifold with boundary subject to local boundary conditions with the help of heat kernel methods. In even dimensions, we relate this invariant to η-invariants of a boundary Dirac operator, while in odd dimension, it is expressed through the index of boundary operators. We stress the necessity of the strong ellipticity condition for the applicability of our methods. We show that the Witten--Yonekura boundary conditions are not strongly elliptic, though they are very close to strongly elliptic ones. This talk is based on a joint work with A. V. Ivanov (POMI), arXiv:2208.00476.
In an attempt toward a better understanding of the vacuum of QCD I propose a condensation of the tachyonic mode in SU(2). In the Savvidy vacuum, this mode is known to be unstable. In an approximation where the gluon fields are reduced to the tachyonic mode, which can be considered as a complex scalar field in (1+1)-dimensions, I apply the methods known from the Higgs model and finite temperature field theory. The symmetry is spontaneously broken by a condensate of tachyons, i.e. of the unstable mode. As a result, I obtain a stable vacuum state with energy below zero. The energy of this state is a minimum in two parameters, the chromomagnetic background field, and the condensate. Raising the temperature, I observe a phase transition; and a restoration of the symmetry. (based on arxiv 2207.08711)
The talk is devoted to an explicit cutoff regularization of the Green's function for a covariant Laplace operator. It is planned to give definitions, explain properties (spectral representation, homogenization, covariance), and formulate results for the case of the four-dimensional Yang-Mills theory.
Schwinger-Keldysh diagram technique is usually involved in the calculation of real-time in-in correlation functions. In the case of thermal state, one can analytically continue imaginary time Matsubara correlation functions to real times. However, not all real-time correlation functions can be obtained by such procedure. Moreover, the numerical analytic continuation is an ill-posed problem. Thus, even in the case of thermal state one may need for Schwinger-Keldysh formalism. If the potential of the system admits degenerate minima, instantonic effects enter the game, so one should also integrate over instantonic moduli space, including the one, corresponding to the imaginary time translational invariance. However, Schwinger-Keldysh closed time contour explicitly breaks such invariance. We argue, that this invariance must be recovered, and show, how it can be done. After that, we construct an extension of Schwinger-Keldysh diagram technique to instantonic systems and demonstrate it on some instructive examples.
We discuss the possibility that bubbles of a parity breaking hadronic medium may emerge in the central heavy ion collisions. After reviewing the methods to describe the mesons on a background with chiral imbalance such as effective field theories and holographic techniques, we discuss the influence of the boundaries on the vector meson propagation. We argue for the existence of the currents localized in the vicinity of the transition region between regions with different axial chemical potential values.
Our research is dedicated to studying the composite Higgs model in the framework of a soft-wall holography. The Higgs field arises as the pseudo-Goldstone mode corresponding to a dynamical symmetry breaking in a new strongly coupled sector leading to a first order phase transition. The bubble nucleation in the early universe can occur in this instance. We present the perturbation theory approach for the homogeneous solutions.
The preprint with the main results has been published at arxiv.org/abs/2209.02331
One-loop electroweak radiative corrections to dilepton production in hadron collisions via photon fusion for Large Hadron Collider (LHC) experimental program are estimated, the most attention is paid to hard bremstrahlung. Discussed reaction follows the Drell-Yan process, its studying is the actual task of LHC experimental program. Detailed numerical analysis of electroweak radiative effects to observable quantities (cross sections and forward-backward asymmetry) in wide kinematical region including the CMS LHC experiment in Run3/HL regime corresponding ultra-high energies and dilepton invariant masses is performed.
The dominant radiative transitions of the charmonium low-lying excited states as well as strong decays of a heavy exotic charmonium-like state have been studied within a covariant quark model by involving the analytic confinement concept. We use the compositeness condition to eliminate any constituent degrees of freedom from the space of physical states and strictly fix the renormalization couplings of the hadron states. The helicity amplitudes, or the Lorentz structures, have been used to express the gauge invariant transition amplitudes of the processes under consideration. Only one adjustable parameter common for the charmonium states $\eta_c({}^1\!S_0)$,$J/\psi({}^3\!S_1)$, $\chi_{c0}({^{3}}\!P_{0})$, $\chi_{c1}({^{3}}\!P_{1})$, $h_c({^{1}}\!P_{1})$, and $\chi_{c2}({^{3}}\!P_{2})$ has been introduced to describe the quark distribution inside the hadron. This parameter is proportional to the ratio between the charmonium's "size" and its physical mass. In doing so, we keep other basic model parameters. Then, we calculated the fractional widths of one-photon radiative decays for states $J/\psi({}^3\!S_1)$, $\chi_{cJ}({^{3}}\!P_{J}),~J=\{0,1,2\}$ and $h_c({^{1}}\!P_{1})$. Our estimated results are in good agreement with the latest data [1].
We have also investigated the strong decay of the exotic charmonium-like state $Y(4230)$, recently reported by the BES-III collaboration. Hereby, the decay modes $Y \to J/\psi \, \pi^+ \pi^-$ and $Y \to J/\psi \, K^+ K^-$ have been considered by interpreting $Y(1^{--})$ as a four-quark hadron. The preliminary results on the decay widths of the processes under consideration are reasonable.
[1]. G. Ganbold, T. Gutsche, M.A. Ivanov, V.E. Lyubovitskij, \
{\it 'Radiative transitions of charmonium states in the covariant confined quark model'}, \
Phys. Rev. D 104 (2021) 094048.
The field theoretic renormalization group is applied to the strongly nonlinear stochastic advection-diffusion equation. The turbulent advection is modelled by the Kazantsev–Kraichnan “rapid-change” ensemble. As a requirement of the renormalizability, the model necessarily involves infinite number of coupling constants (“charges”). The one-loop counterterm is calculated explicitly.
The corresponding renormalization group equation demonstrates existence of a pair of two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain infrared attractive regions, the problem allows for the large-scale, long-time scaling behaviour.
For the first surface (advection is irrelevant), the critical dimensions of the scalar field \Delta_{\theta}, the response field \Delta_{\theta'} and the frequency \Delta_{Omega} are nonuniversal (through the dependence on the effective couplings) but satisfy certain exact identities. For the second surface (advection is relevant), the dimensions are universal and they are found exactly.
Using a simple model of self-organized criticality, we study interplay between intrinsic dynamics and external disturbances that affects the resulting critical behaviour. The model is Hwa-Kardar “running sandpile” that is a stochastic equation for a coarse-grained field that describes evolution of anisotropic system [Phys. Rev. Lett. 62, 1813 (1989); Phys. Rev. A 45, 7002 (1992)]. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we cast the equation into a field theory that can then be studied with the renormalization group analysis. The latter allows one to explore critical points that determine universality classes and related critical exponents. The model is augmented by addition of random motion of the environment modelled by Gaussian velocity ensembles or by the Navier-Stokes stochastic equation. While chaotic external flows are known to dramatically affect critical behaviour, we found that it is a contest between strongly anisotropic intrinsic dynamics and isotropic external disturbances that produce the most interesting results. Isotropic flow may “wash away” the anisotropy of the system altogether but surprisingly it does not always preclude the restoration of original strong anisotropy via highly nontrivial mechanism. New crossover universality class can also appear where the anisotropy survives, but becomes “weakened” in a sense that there is no longer two independent dimensions corresponding to different directions. Anisotropic flow, on the other hand, brings interesting results when Hwa-Kardar model is altered to include a columnar (time-independent or spatially quenched) random noise instead of the white noise. Fixed points in this case turn out to have overlapping stability regions; the situation may be interpreted as a universality violation. It is especially interesting that the same model without external flow does not predict this.
Diffusion-limited reactions are famous examples of nonlinear statistical systems and can be observed in various chemical, biological and physical problems. For these systems in low space dimensions, the usual description by means of kinetic rate equations is not sufficient and the effect of density fluctuations has to be taken into an account. Using perturbative renormalization group we study a specific multi-species reaction-diffusion system with reactions $\textit{A} +\textit{A} \rightarrow (\emptyset, A),$ $\textit{A} +\textit{B} \rightarrow \textit{A}$ at and below its critical dimension $d_c = 2$. In particular, we investigate the effect of thermal fluctuations on reaction kinetics. These are generated by means of a random velocity field modelled by a stochastic Navier-Stokes equations. The analysis is performed by means of field-theoretic renormalization group and explicit calculations are restricted to the one-loop order in the perturbation theory.
We investigate massive models of quantum field theory of scalar field in logarithmic dimensions in Euclidean space. The Schwinger-Dyson equation and non-trivial solution for mass are considered in the paper.
The Schwinger-Dyson equation has the form:
D−1=Δ−1−Σ
where D is a full propagator, Δ is a bar propagator, Σ is a self-energy operator. In the minimal subtraction (MS) scheme it holds:
Δ(p)=1p2
where p is a momentum. The inverse full propagator has the following characteristic:
⎧⎩⎨D−1(p)|p2=−m2=0(∂∂(p2)D−1(p))∣∣p2=−m2=1A.
In the main approximation of perturbation theory it holds:
D(p)=Ap2+m2
where A is an amplitude, m is a mass. We investigate the scalar models ϕ3, ϕ4 and ϕ6. For the theories ϕ3 and ϕ4 mass appears in the first order of perturbation theory whereas for the ϕ6-theory the mass does not appear in the first order.
To be held in EIMI
The Hawking temperature for Schwarzschild black hole $T_H=1/8\pi M$ is
singular in the limit of vanishing mass $M\to 0$. However, the
Schwarzschild metric itself is regular when the black hole mass $M$ tends
to zero, it is reduced to the Minkowski metric and there are no reasons to
believe that the temperature becomes infinite.
We will discussed how to improve the situation and avoid this
discrepancy.
The current status of experimental tests of quantum electrodynamics with heavy ions is briefly reviewed. Special attention is focused on tests of QED in
supercritical regime. According to the standard QED theory, in slow collisions of two bare nuclei with the total charge number larger than the critical value, Z_1+Z_2 > Z_c =173, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. Detection of the spontaneous positron emission would be the direct evidence of this fundamental phenomenon. However, the
spontaneous positron emission is generally masked by the dynamical positron
emission, which is induced by a strong time-dependent electric field created
by the colliding nuclei. For many years it was believed that the vacuum
decay can be observed only in collisions with nuclear sticking, when the
nuclei are bound for some period of time due to nuclear forces. In our recent papers [1,2], it was shown that the vacuum decay can be observed without any sticking of the nuclei. This can be done via measurements of the pair-production probabilities or the positron spectra for a given set of nuclear trajectories. The results of this study will be presented in the talk.
References
[1] I.A. Maltsev, V.M. Shabaev, R.V. Popov, Y.S. Kozhedub, G. Plunien,
X. Ma, and Th. Stöhlker, and D.A. Tumakov, Phys. Rev. Lett. (2019), 123 ,
113401.
[2] R.V. Popov, V.M. Shabaev, D.A. Telnov, I.I. Tupitsyn, I.A. Maltsev,
Y.S. Kozhedub, A.I. Bondarev, N.V. Kozin, X. Ma, G. Plunien, Th. Stöhlker,
D.A. Tumakov, and V.A. Zaytsev, Phys. Rev. D (2020), 102, 076005.
Abstract: Good understanding of dense quark matter(tree-color QCD) is crucial for lots of physical applications. For instance, it is important for different astrophysical and cosmological problems and modern heavy ion collision experiments. It is known that dense quark matter is strongly interacting system. For this reason it is difficult to obtain reliable results of its study within different phenomenological models. Unfortunately because of the sign problem the most powerful approach to study strongly interacting systems - lattice simulation - is not applicable at sufficiently large density. However, there are physical systems which have properties similar to tree-color QCD and they are free from the sign problem. Two-color QCD is an example of such system. In this report we are going to review the results of the studies of dense two-color QCD which were obtained within lattice simulations. The phase transitions in this system as well as properties of dense matter will be reviewed.
We shortly review progress in multilloop RG calculations achieved
after 2017 when the 5-loop QCD beta-function was first announced. We also
provide an update of developments related to the recently decoded
transcendental structure of MS-scheme beta-functions and anomalous dimensions.
The three-loop $\beta$-functions for the Minimal Supersymmetric Standard Model (MSSM) are obtained in case of using the higher covariant derivative regularization for an arbitrary supersymmetric subtraction scheme. Firstly, the anomalous dimensions defined in terms of the bare couplings are calculated for all MSSM chiral matter superfields. After that, using the NSVZ relations we construct the three-loop $\beta$-functions also defined in terms of the bare couplings. This is possible, because in all orders the NSVZ equations are satisfied for these renormalization group functions with the higher covariant derivative regularization. Next, expressions for the two-loop anomalous dimensions and for the three-loop $\beta$-functions standardly defined in terms of the renormalized couplings are obtained for an arbitrary renormalization prescription. For a certain subtraction scheme, we reproduce the $\overline{DR}$-result obtained earlier, thus verifying it by an independent calculation.
We study the possibility of the existence of the QCD CBK relation and its multiple-beta function representation in the gauge-invariant static potential motivated effective V-scheme at the four-loop level. This representation provides
interesting relations between definite terms of {\beta}-expanded coefficients
of Static potential, Adler D-function and Bjorken polarized sum rule.
The corresponding terms of the studied {\beta}-expansion are fixed. Possible further applications are commented.
We demonstrate how to use our general result for the renormalization-group functions to compute the anomalous dimensions of various operators in a range of specific scalar models. Recent applications include the calculation of the scaling dimensions of different tensor operators in $O(n)$-symmetric and hypercubic theories.
We study a self-organized critical system under the influence of turbulent motion of the environment. The model addresses two unusual scaling regimes (types of critical behaviour) predicted by the field-theoretic renormalization group analysis for a self-organized critical system with turbulent motion of the environment. The system is modelled by the anisotropic stochastic equation for a running sandpile'' introduced by Hwa and Kardar in [{\it Phys. Rev. Lett.} {\bf 62}: 1813 (1989)]. The turbulent motion is described by the isotropic Kazantsev-Kraichnan
rapid-change'' velocity ensemble for an incompressible fluid. The original Hwa-Kardar equation allows for independent scaling of the spatial coordinates $x_{\parallel}$ (the coordinate along the preferred dimension) and ${\bf x_{\bot}}$ (the coordinates in the orthogonal subspace to the preferred direction) that becomes impossible once the isotropic velocity ensemble is coupled to the equation. However, it is found that one of the regimes of the system's critical behaviour (the one where the isotropic turbulent motion is irrelevant) recovers the anisotropic scaling through dimensional transmutation.'' The latter manifests as a dimensionless ratio acquiring nontrivial canonical dimension. The critical regime where both the velocity ensemble and the nonlinearity of the Hwa-Kardar equation are relevant simultaneously is also characterized by
atypical'' scaling. While the ordinary scaling with fixed IR irrelevant parameters is impossible in this regime, the ``restricted'' scaling where the times, the coordinates, and the dimensionless ratio are scaled becomes possible. This result brings to mind scaling hypotheses modifications for systems with significantly different characteristic scales.
The phenomenon of self-organized criticality (SOC) consists in the emergence of scaling in open nonequilibrium systems with dissipative transport. Unlike equilibrium systems that arrive at critical states when control parameters approach their critical values, systems with SOC evolve to critical states due to their intrinsic dynamics. Such systems are widespread in nature with SOC being observed in physical, biological, economic and social systems. Critical behavior of stochastic system can be drastically affected by turbulent motion of the environment, thus, it is important to study the motion influence on systems with SOC. In this report, it was presented a field theoretic renormalization group analysis of the continuous anisotropic model of SOC introduced in (a ”running sandpile”) coupled to the stochastic Navier–Stokes equation. The model provides an example of competition between strongly anisotropic intrinsic dynamics and external isotropic disturbance by the turbulent environment.
Quantum dynamics of boson gas near the Bose-Einstein condensation transition has attracted considerable interest recently. While the static critical behavior of the system is generally believed to belong to the universality class of the $XY$ model, [or $O(2)$ model] with the corresponding critical exponents, there is no consensus about its dynamic critical behavior and, in particular, the value of the dynamic critical exponent z. Classical papers suggest that systems with such behaviour must be described by phenomenological models of stochastic dynamics. However, due to the technical difficulties that arises in these models, there is no unambiguous answer for the dynamic critical exponent responsible for dynamic critical behaviour of the system. In our work we propose a microscopic model based on framework of time-dependent Green's function at finite temperature. With using this approach we were able to construct adequate IR model for obtaining corresponding dynamic critical exponent $z$. Surprisingly, at an unique IR stable fixed point our model become equivalent to the model $A$ of stochastic dynamics. Such coincidence lead us to revisiting stochastic model $F$. It turns out that taking into account incompressibility effects reduce model $F$ to the same model $A$. In this talk I am going briefly discuss framework of time-dependent Green's function at finite temperature then describe construction of IR effective model. Afterwards I present results of two and three loops calculation and corresponding RG analysis. Also I probably shortly discuss effects of incompressibility for stochastic field models.
Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory. Explicit examples of non-abelian fermionic T-dualities that produce real backgrounds are given. Some of our examples can be bosonic T-dualized into usual supergravity solutions, while the others are genuinely non-geometric. We establish interesting connection between ordinary and generalized supergravities through the consecutive non-abelian fermionic and bosonic T-dualities.
Horndeski theories [1]
\begin{align}
&S=\int\mathrm{d}^4x\sqrt{-g}\left(\mathcal{L}2 + \mathcal{L}_3 + \mathcal{L}_4 + \mathcal{L}_5 + \mathcal{L{BH}}\right),\
&\mathcal{L}2=F(\pi,X),\
&\mathcal{L}_3=K(\pi,X)\Box\pi,\
&\mathcal{L}_4=-G_4(\pi,X)R+2G{4X}(\pi,X)\left[\left(\Box\pi\right)^2-\pi_{;\mu\nu}\pi^{;\mu\nu}\right],\
&\mathcal{L}5=G_5(\pi,X)G^{\mu\nu}\pi{;\mu\nu}+\frac{1}{3}G_{5X}\left[\left(\Box\pi\right)^3-3\Box\pi\pi_{;\mu\nu}\pi^{;\mu\nu}+2\pi_{;\mu\nu}\pi^{;\mu\rho}\pi_{;\rho}^{\;\;\nu}\right],\
&\mathcal{L_{BH}}=F_4(\pi,X)\epsilon^{\mu\nu\rho}{\quad\;\sigma}\epsilon^{\mu'\nu'\rho'\sigma}\pi{,\mu}\pi_{,\mu'}\pi_{;\nu\nu'}\pi_{;\rho\rho'}+
\\nonumber&\qquad+F_5(\pi,X)\epsilon^{\mu\nu\rho\sigma}\epsilon^{\mu'\nu'\rho'\sigma'}\pi_{,\mu}\pi_{,\mu'}\pi_{;\nu\nu'}\pi_{;\rho\rho'}\pi_{;\sigma\sigma'},
\end{align}
are the most general scalar-tensor theories of gravity, which has second-order equations of motion and thus erasing the Ostrogradsky instability. In addition, it was found that in this theory the null energy conditions (NEC) are not related to the stability of cosmological solutions. This fact allows one to construct healthy NEC-violating genesis and bounce solutions, as well as new models of dark energy and inflation with interesting phenomenology [2].
However, the construction of non-singular cosmological solutions is prevented by the so-called no-go theorem [3]. In our talk we present a classification of solutions that avoid the no-go theorem.
[1] G.W. Horndeski, "Second-order scalar-tensor field equations in a four-dimensional space," Int. J. Theor. Phys. 10 (1974), 363-384. doi:10.1007/BF01807638
[2]V.A. Rubakov, "The Null Energy Condition and its violation," Phys. Usp. 57 (2014), 128-142. doi:10.3367/UFNe.0184.201402b.0137. [arXiv:1401.4024 [hep-th]].
[3] S. Mironov, V. Rubakov and V. Volkova, "Bounce beyond Horndeski with GR asymptotics and $\gamma$-crossing," JCAP 10 (2018), 050. doi:10.1088/1475-7516/2018/10/050. [arXiv:1807.08361 [hep-th]].
The main subject of study in the general relativity and other branches of science is the geometry of (pseudo)-Riemannian spaces defined by a metric. To better imagine and understand the properties of a particular spacetime, it is often useful to define a surface in some ambient space that has such a metric - in other words, to construct an isometric embedding. However, the search for an explicit form of such surfaces turns out to be a very nontrivial problem of solving a system of nonlinear PDEs. Fortunately, this problem is greatly simplified if the spacetime under study has sufficiently rich symmetry (which is the case for many physically interesting spacetimes). This talk is devoted to a method of construction of surfaces with a given metric, which based on a group-theoretic analysis of the symmetries of this metric. Several examples of its application will be discussed (Friedmann and Godel universes, rotating black holes etc.) along with its possible generalizations.
We present an off-shell formulation of ${\cal N}=2$ higher spin supermultiplets within the harmonic
superspace approach. Each supermultiplet is described by a triple of unconstrained harmonic analytic
gauge superfields, with the linearized action of some universal form. To the first order in gauge superfields,
we give their off-shell cubic couplings to ${\cal N}=2$ matter hypermultiplets and define the higher-spin gauge
transformations of the latter. Some further prospects of this new direction of applications of the harmonic
superspace approach are discussed in brief.\
The talk is based on two recent works with Ioseph Buchbinder and Nikita Zaigraev, JHEP 2021, 2022.
Massless irreducible representations of the Poincaré group in the six-dimensional Minkowski space are studied.
It is shown that the finite spin representation is defined by two integer or half-integer numbers
while the infinite spin representation is defined by the real parameter and one integer or half-integer number.
Massless infinite spin irreducible representations in the space of the two-twistor fields are constructed and
a full set of equations of motion for such fields is found.
A field twistor transform is constructed and infinite spin fields are found in the space-time formulation with an additional spinor coordinate.
A new 6D infinite spin field theory in the light-front formulation is presented.
The found infinite-spin fields in the light-cone frame depend on two sets of the SU(2)-harmonic variables.
The generators of the 6D Poincaré group and the infinite spin field action in the light-front formulation are presented.
The resonant process of the creation of an ultrarelativistic electron–positron pair by two hard gamma quanta in a strong electromagnetic field with intensity up to $10^{27} W/cm^2$ (the Breit–Wheeler process modified by an external field) was theoretically studied. Under resonance conditions, the intermediate virtual electron (positron) in the external field comes on the mass shell. As a result, there are four reaction channels for the process instead of two. For each of those channels, the initial process of the second order in the fine structure constant effectively reduces into two successive processes of the first order: the external field-stimulated Breit–Wheeler process and the external field-stimulated Compton effect. The resonant kinematics of the process was also studied in detail. The process had characteristic threshold number of absorbed gamma quanta from an external field, and all initial and final particles had to be ultrarelativistic and propagate in a narrow cone. Furthermore, the resonant energy spectrum of the electron-positron pair significantly depended on emission angles. Clearly, there was a qualitative difference between resonant and non-resonant cases. Lastly, the resonant differential probability of studied process was obtained. The resonant differential probability significantly exceeded the non-resonant one without the external field. Theoretical predictions can be tested in international research projects (SLAC, FAIR, XFEL, ELI, XCELS).
According to quantum electrodynamics, a strong electromagnetic field can make the vacuum state decay via the production of electron-positron pairs. This process is accompanied by the emission of soft photons and generation of higher-order harmonics. These two radiation channels are described within the leading order by vertex and tadpole Feynman diagrams. Here we evaluate and discuss both of these contributions. The interaction between the quanitzed Dirac field and the external (laser) background is taken into account exactly, i.e., within the Furry picture. To obtain quantitative predictions in the domain of realistic field parameters, we employ the WKB approach. Also, it is shown that the presence of photons in the initial state gives rise to an additional (stimulated) channel of photon emission besides the pure vacuum one. We propose an experimental scenario for measuring this additional signature in order to indirectly probe the pair-production mechanism in the nonperturbative regime.
We derive the full set of beta functions for the marginal essential
couplings of projectable Horava gravity in $(3+1)$-dimensional
spacetime. To this end we compute the divergent part of the one-loop
effective action in static background with arbitrary spatial
metric. The computation is done in several steps: reduction of the
problem to three dimensions, extraction of an operator square root from
the spatial part of the fluctuation operator, and evaluation of its
trace using the method of universal functional traces. This provides
us with the renormalization of couplings in the potential part of the
action which we combine with the results for the
kinetic part obtained previously. The calculation uses
symbolic computer algebra and is performed in four different gauges
yielding identical results for the essential beta functions. We
additionally check the calculation by evaluating the effective action
on a special background with spherical spatial slices using an
alternative method of spectral summation. We conclude with a
preliminary discussion of the properties of the beta functions and the
resulting renormalization group flow, identifying several candidate
asymptotically free fixed points.
Helicity amplitudes in with massive fermions can be written in tensor form using 4-component spinors (bi-spinors). The approach is demonstrated using the examples of hard Bremsstrahlung processes for future $e^+e^-$ colliders.
We investigate properties of four-point colour ordered scattering amplitudes in
D=6 fishnet CFT. We show that these amplitudes are related via a very simple
relation to their four-dimensional counterparts. Exploiting this relation, we obtain a closed expression for these amplitudes and investigate its behaviour at weak and strong coupling in different kinematic regimes.
We discuss the microscopical justification of dissipation in model nonrelativistic Fermi and Bose systems with weak local interaction above phase transitions. Dynamics of equilibrium fluctuations are considered in Keldysh – Schwinger framework. We show that dissipation is related to pinch singularities of diagram technique. Using Dyson – Schwinger equation and two loop approximation we define and calculate attenuation parameter which is related to exponentiality of Green’s functions decay. We show that the attenuation parameter is the microscopic analogous of the Onsager kinetic coefficient and it is related to attenuation in excitation spectrum.
The usual Vaidya spacetime may be extended to include both null dust and null string fluids leading to the generalised Vaidya spacetime. Nowadays, this metric is widely used to describe the gravitational collapse, a radiating star with a generalised Vaidya atmosphere, black holes in dynamical cosmology backgrounds. In our work we consider horizon structure of this spacetime. We have calculated the conformal Killing vector in order to specify the mass function $M(v,r)=\lambda v+\mu v^{2\alpha}r^{1-2\alpha}$, where $\alpha$ is from the equation of the state $p=\alpha \rho$. We impose the energy conditions to obtain conditions for $\lambda$, $\mu$ and $\alpha$. Also we calculate the apparent horizon, the putative horizon, the event horizon. We find the the coordinate transformation to the static coordinates. The properties of generalized Vaidya spacetime in static coordinates is investigated. We consider particular models when $\alpha=0$ - the dust case, $\alpha=\frac{1}{3}$ - the electro-magnetic field, $\alpha=-1$ - De Sitter solution and $\alpha=1$ - the stiff fluid.
We considered the Tsallis holographic dark energy model in frames of Nojiri-Odintsov gravity with $f(R)=R+\lambda R^2-\sigma{\mu}/{R}$. The equations describing the cosmological evolution in this case contain third derivative of the scale factor on time. Therefore this requires to impose initial condition on the second derivative $a$ (which is equivalent to the condition on $\dot{H}(0)$). The cosmological evolution of such universe is investigated for various initial conditions and values of parameters. The evolution of the universe is studied in detail for the case when $\dot{H}(0)$ coincides with the value in the standard cosmological model with $\Omega_\Lambda = 0.72$. Solutions have interesting feature namely Hubble parameter ``oscillates'' near dependence corresponding to THDE in General Relativity. The amplitude of this oscillations grows with time in future. For $\mu\neq 0$ a future singularity arises corresponding to zero of second derivative of $f(R)$ for some $R$. It is shown that for $\mu \neq 0$ appearance of singularities are typical and the time up to these singularities can be relatively small from cosmological viewpoint. The singularity is associated with the zero of second deribative of $f(R)$ on $R$. Dynamics of the universe in the past is not especially sensitive to this initial condition and is close to that in the model of holographic dark energy in the background of GTR (the differences appear only at times close to the initial singularity of the Big Bang). Our analysis shows that such models for some parameters can describe observational data for SN Ia and dependence $H(z)$ with sufficient accuracy especially for $\gamma=1$ and larger values of $\dot{H}$ in comparison with $\Lambda$CDM model. Also one note that $H(z)$ data are described better in frames of THDE on modified gravity backgroud. This means that the models considered by us can be quite realistic.
Penrose process states that due to collision or decay there might be particles with negative energy in the ergosphere of a rotating black hole. Recently, the analogue of this process has been found for charged particles in Reissner-Nordstrom spacetime.
In this work the Penrose process is considered for charged particles in charged Vaidya spacetime. This metric is dynamical one with mass and charge are being functions of time. We use conformal Killing vector to specify the mass and charge functions in order to transform the metric to the static coordinates. We define the generalized ergosphere for charged particles with negative energy and investigate the properties of such particles. Finally, we compare results with ones obtained for Reissner-Nordstrom spacetime.
We consider dynamics of the massive minimally coupled scalar field theory in an expanding Friedmann-Lemaitre-Robertson-Walker universe. We consider the standard toy model of the conformally flat space-time where the conformal factor becomes constant at the distant past and the distant future. Employing Schwinger-Keldysh diagrammatic technique, we compute infrared loop corrections to the occupation number and anomalous quantum average of the scalar field and show that these corrections are growing with time. Using these observations, we demonstrate that the regularized stress-energy tensor at the distant future acquires substantial quantum corrections which exceed the long known tree-level contributions to the particle flux.
Техника функциональных преобразований Лежандра дает возможность получить для функций Грина квантововолевой системы уравнения в виде бесконечной суммы скелетных диаграмм Фейнмана. Если для вывода этих уравнений используется преобразование Лежандра порядка n>1, линиям этих графиков соответствуют полные пропагаторы, а вершинам порядка k<n+1 - полные к-точечные функции Грина. Учет в скелетных уравнения их начальных приближений, дает возможность получения приближенных нелинейных интегральных уравнений для функций Грина, которые можно использовать для поиска нетривиальных решений квантовополевых задач,
для которых неприменима теория возмущений. В докладе дается обзор применения таких методов для расчетов описывающих скейлинг характеристик поведения моделей квантовой теории поля в критической точке.
No computation can be performed without first identifying the underlying field theory. For some physical systems this is challenging.
He we give examples where the effective action for a class of disordered systems is measured in simulations and experiments.
This allows one to identify, and finally construct, the appropriate field theory. While we apply these ideas to the quenched Edwards-Wilkinson and quenched KPZ equation,
the method may be useful more generally.
Time dependent at finite temperature Green functions were used to describe the dynamics of the phase transition of quantum Bose systems to the superfluid state. The obtained renormalization group results contradict the currently accepted dynamic stochastic model E for this phenomenon. With the help of Temperature Green functions, a new model of the phase transition of Fermi systems to the superconducting state was created. The renormalization group results testify in favor of a high phase transition temperature in layered or heterogeneous conductors, which is confirmed experimentally.
General issues of introduction of temperature Green's functions are also discussed.
It is common opinion that the rotation into the Euclidean
space turns quantum field theory into an equilibrium
statistical physics. But each classical science corresponds to a set of quantum ones. The statistical equilibrium theory corresponds to the single correct only. The report will show that equilibrium statistical physics not only loses the property of Lorentz invariance (due to the use of a co-moving coordinate system), but also fundamentally distinguishes between "partitial" and "wave" descriptions of systems (in the sense of formalisms of the first and second order in time). It is argued that preference should be given to the first-order formalism, which rejects oscillatory types models.
Particles with negative energies are considered for three different cases: inside of horizon of nonrotating Schwarzschild black hole, Milne's coordinates in flat Minkowski space-time (Milne's universe using nonsynchronous coordinates) and in cosmological Godel model of the rotating universe. It is shown that differently from the Godel model with nondiagonal term where it occurs that negative energies are impossible they are present in all other cases considered in the paper. Particles with zero energy are also possible in first two cases.
The mystery of the nature of dark matter is one of the most
interesting problems of modern theoretical physics. The lack of
progress in attempts to directly detect dark matter allows us to
assume that all effects related to dark matter are purely
gravitational. The key idea of such an approach is to switch from GR
to some modified theory of gravity with more general equations than
the Einstein equations. If new equations can be written as Einstein
equations with an additional contribution in the r.h.s., then some of
the degrees of freedom of the modified gravity appear to be
responsible for dark matter which turns out to be fictitious. The
comparison of the properties of this fictitious matter arising in
considered modified gravity with the observable properties of dark
matter gives the opportunity to verify the theory. The most known
example of such modified gravity is the mimetic gravity. However, the
mimetic gravity in its simplest form leads to fictitious matter with a
too small number of degrees of freedom. In order to describe all
observable properties of dark matter the mimetic gravity should be
significantly complexified by introducing additional parameters and
terms into the action of the theory. Another example of an appropriate
modified theory of gravity is Regge-Teitelboim's embedding theory
giving essentially nontrivial fictitious matter right away. On the
other hand, the description of gravity in terms of embedding theory
has a clear geometric sense closely related to the one utilized in the
fundamentals of the string theory. The key idea of the embedding
approach is to suggest that the time-space is a curved 4-dimensional
surface in a flat 10-dimensional ambient space. Since the usual
Einstein-Hilbert action is used the embedding gravity doesn't contain
any additional parameters. The properties of the fictitious matter in
this approach can be compared with the observed properties of dark
matter on the cosmological and galactic scales as well. For the
convenience of comparison, one can reformulate the embedding gravity
in a form of GR with additional contributions at the level of choice
of action and degrees of freedom. Also, a method can be proposed to
analytically estimate the possibility of core or cusp density profile
origin in galaxies in order to gather more precise information about
dark matter behavior.
The Landau-Khalatnikov-Fradkin (LKF) transformation is a
powerful and elegant transformation allowing to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a non-perturbative identity between massless propagators in two different gauges. In the case of quenched three-dimensional QED, from the LKF identity, assuming the finiteness of the perturbative expansion, we
state that, exactly in d=3, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge. To check the result, we calculate the three- and four-loop corrections to the massless fermion propagator. The three-loop correction is finite and gauge invariant but, however, the four-loop one has singularities except in the Feynman gauge where it is also finite. These results explicitly show an absence of the finiteness of the perturbative expansion in quenched three-dimensional QED. Moreover, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the LKF transformation.
In this talk I'll discuss a holographic probes of a rotating $\mathcal{N}=4$ SYM quark-gluon plasma. Following the holographic duality a 4d rotating strongly-coupled QGP can be described by a rotating Kerr-AdS_5 black hole. The Kerr-AdS_5 black hole has a conformal boundary $R\times S^{3}$, on which the $N=4$ SYM theory (a thermal ensemble) "lives". Moreover, the Hawking temperature corresponds to the temperature of the dual theory. We study rectangular Wilson loops in $N=4$ SYM on $R\times S^{3}$ at finite temperature using the holographic dictionary. According to this we consider an open string in Kerr-AdS_5 hanging down from the conformal boundary to the horizon, so the string endpoints correspond to quarks. We calculate the quark-antiquark potential from the Nambu-Goto action of the string. We show that the potential includes the Coulomb and linear parts, which indicates about a confinement/deconfinement phase transition. We also calculate the jet-quenching parameter of a fast patron in the rotating $\mathcal{N}=4$ SYM QGP and analyze its dependence on the rotation. We show that the value of the jet-quenching parameter for the rotating case can be smaller comparing to the case of the planar AdS black hole.
We propose a method for constructing equations of generalized 10D supergravity using non-unimodular bi-Killing Yang–Baxter deformations. The presented approach is generalized to the 11-dimensional case. Using non-unimodular three-
Killing generalized Yang–Baxter deformations, a generalization of the equations of 11D supergravity is obtained.
We consider the massless and massive theory of higher spin (HS) fields within the BRST approach and construct a (off-shell) general cubic interaction vertices corresponding to the irreducible HS fields on the d-dimensional flat spacetime. To this end, we develop a concept of deformation Noether's procedure of free gauge theory on a base of BRST approach with complete BRST operator.
As compared to previous works on cubic vertices, which did not take into account sequentially traceless constraints, we use the complete BRST operator,
\begin{eqnarray}
Q =
\eta_0l_0+\eta_1^+l_1+l_1^{+}\eta_1+
\eta_{11}^+\widehat{L}{11}+\widehat{L}{11}^{+}\eta_{11} +
{\imath}\eta_1^+\eta_1{\cal{}P}_0
,\end{eqnarray}
which includes trace constraints $\widehat{L}_{11}$ (and its dual) $\widehat{L}_{11}^{+}$ necessary to describe together with differential constraints (d;Alambert $l_0$, divergence $l_1 $ and its dual $l_1^{+}$) irreducible representations of Poincare group with integer spins $s$. $Q$
(used here to find gauge-invariant Lagrangian formulation for initial non-Lagrangian equations) depends,on the Grassmann-odd ghost operators $\eta_0, \eta_1^+,\eta_1,
\eta_{11}^+,\eta_{11}$, ${\cal P}_0$, ${\cal P}_{1}$, ${\cal P}^+_{1},$ ${\cal P}_{11},{\cal P}^+_{11}$.
As a result, we covariantize the cubic vertices given as three-vectors in oscillator representation $\big| V^{(3)}\rangle^{(m)_3}_{(s)_{3}}$, firstly found in light-cone formalism [R.Metsaev, Nucl. Phys.B 759 (2006) 147] with preserving the irreducibility for the fields on the interacting level with the same (as for dynamics of free fields) numbers of physical degrees of freedom for each copy of interacting higher spin fields incorporated into field vectors from the respective Fock space. The operator of cubic vertex satisfies to the properties of BRST and spin closeness
\begin{equation}
\sum_i Q^{(i)}
\big|{V}{}^{(3)}\rangle^{(m)3}{(s)3} =0, \qquad
\sigma^{(i)}\big|{V}{}^{(3)}\rangle^{(m)_3}{(s)_3} \ =\ 0,
\end{equation}
(for $i=1,2,3$ enumerating the copy of fields, masses $(m)_3=(m_1,m_2,m_3)$ and spins $(s)_3=(s_1,s_2,s_3)$).
As compared to the covariant form of the vertices obtained with using BRST approach with incomplete BRST operator [R.Metsaev,Phys. Lett. B 720 (2013)
237], the interacting theory with complete BRST operator leads to new contributions to the vertex that contain additional terms with fewer space-time derivatives of fields, as well as with multiple trace contributions.
We found the general solution for the equations above, for interacting, first, massless higher spin fields, with helicities $(s_1,s_2,s_3)$ in [I.L. Buchbinder, A. Reshetnyak, Phys. Lett. B 820 (2021) 136470], second, one massive with mass and spin $(m,s_1)$ and two massless fields
with $(0,s_2)$, $(0,s_3)$, third, two massive and one massless higher spin fields both for general case of different masses and for critical case of coinciding masses.
Cosmological particle creation: Weyl geometry + Scalar field
Victor Berezin
Institute for Nuclear Research of the Russian Academy of Sciences,
60th October Anniversary Prospect 7a, 117312 Moscow, Russia
E-mail: berezin@inr.ac.ru
Abstract
We investigated the possibility of the homogeneous and isotropic cosmological solution in Weyl geometry, which differs from the Riemannian geometry by adding the so-called Weyl vector. The Weyl gravity is obtained by constructing the gravitational Lagrangian both to be quadratic in curvatures and conformal invariant. It is found that such solutions may exist provided there exists the direct interaction between the Weyl vector and the matter fields. Assuming the matter Lagrangian is that of the perfect fluid, we found how such an interaction can be implemented. Due to the existence of the quadratic curvature terms and the direct interaction the perfect fluid particles may be created straight from the vacuum, and we found the expression for the rate of their production which appeared to be conformal invariant. In the case of creating the universe “from nothing" in the vacuum state, we investigated the
problem, whether this vacuum may persist or not. It is shown that the vacuum may persist with respect to producing the non-dust matter (with positive pressure), but cannot resist to producing the dust particles. These particles, being non-interactive, may be considered as the candidates for the dark matter.
One of the ways to study the space near a black hole is to study the behavior of a test body in its gravitational field. In this paper, we consider the deviation of geodesics, which is physically responsible for the tidal forces acting on a body in the field of a rotating black hole. The modified geodesic deviation equation in the curved space-time of a axially-symmetric Kerr black hole is analyzed. The main difference between the generalized deviation equation and the classical one is that the test particles can be located at any distance from each other, i.e. geodesics are not infinitely close. For simplicity, it was assumed that particles has only a radial component of the 4-velocity. The analysis revealed that, depending on the distance and velocity of relativistic particles, the sign of tidal forces changes only along the radial component of the tidal acceleration vector.
We describe thermodynamics properties and Hawking-Page phase transition of the Schwarzschild black hole in the Anti-de Sitter-Beltrami (SAdSB) spacetime.
We discuss the Beltrami or inertial coordinates of the Anti-de Sitter(AdS) spacetime. Transformation between the non-inertial and inertial coordinates of the AdS spacetime is introduced to construct the solution of spherical gravitating mass and other physical quantities. The Killing vector is determined to calculate the event horizon radius of this black hole. The entropy and the temperature of SAdSB black hole are determined by the Noether charge method. The Smarr relation and first law of black hole thermodynamics for the SAdSB spacetime have been formulated. The Gibbs free energy and heat capacity of this black hole is calculated and the first-order phase transition between small and large black holes is also discussed. The second-order phase transition between the thermal AdS and the large black hole is also investigated and the Hawking-Page temperature is computed and compared with the case of the Schwarzschild-Anti-de Sitter(SAdS) black hole.
In the last decade, de Sitter (dS) and Anti-de Sitter (AdS) spacetimes have generated a lot of interest. This led to the creation of a new kinds of Special Relativity (SR), the so-called dS-SR and AdS-SR: relativity with dS(AdS) radius $R$. The existence of inertial frames of reference and inertial coordinate systems are the keystones of the SR. It can be proved by direct calculations that the Beltrami coordinates in dS(AdS) are inertial, as are the Cartesian coordinates in the Minkowski space-time The Beltrami coordinates are defined by the ratio of two homogeneous coordinates $x^{\mu}=RX^{\mu}/X^{5}$ or $x^{\mu}=RX^{\mu}/X^{-1}$ when the dS(AdS) spacetimes are embedded in a homogeneous spacetime spanned by $X^A$, $A=\{0,1,2,3,5\}$ or $A=\{-1,0,1,2,3\}$.
The AdS theory differs from the dS theory in that in AdS, in addition to the standard limit $R\to \infty$ leading to the SR theory, there is a possible limit $c\to \infty$ leading to a theory equivalent to the SR, but not containing the constant $c.$ The corresponding spacetime was called $R$-spacetime.
The physics in $R$-spacetime has been considered in sufficient detail earlier. In this report, we will turn to general relativity (GR) in $R$-spacetime. First, an analogue of the Schwarzschild metric in $R$-space will be constructed. With spacetime localization, this metric does not differ from the standard Schwarzschild metric in Minkowski space, but globally these are completely different metrics, since in one of them the speed of light appears only as a scale factor. Next, we will study the various characteristics of black holes in comparison with the Minkowski spacetime
We explicitly construct the Lax pair (L,A) for the N-extended supersymmetric Calogero--Moser models.
Having obtained such a representation, which correctly reproduces all equations of motion, we consider the integrability of these models.
To represent the structure of conserved currents, we derive the complete set of Liouville charges,
which depend on lower powers of momentum, for the supersymmetric N=2 model.The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.
Quantum spin chains and their degenerations, quantum Gaudin models, play an important role in modern mathematics. The study of these integrable models is interlaced with such areas as the representation theory of Lie algebras and their deformations, the quantum cohomology and K-theory of quiver varieties, the geometric Langlands correspondence.
It is natural to study Lie-theoretic constructions using the language of symmetric tensor categories. In the talk, I will apply this philosophy to the quantum rational Gaudin model associated with the Lie algebra $\mathfrak{gl}_{n}$. I will show that there is a natural construction of the higher Gaudin Hamiltonians associated with the Deligne's category $\underline{Rep}(GL_{t})$, $t\in\mathbb{C}$, which can be understood as an interpolation of the category $Rep(GL_{n})$ of finite-dimensional representations of the Lie group $GL_{n}$ to any complex $n$. This construction is a step towards understanding of the Gaudin model associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$.
It is known that the relations in the algebra of higher Gaudin Hamiltonians (the Bethe algebra) are given by certain no-monodromy conditions on a differential operator of order $n$. In the second part of the talk, I will discuss how these conditions can be interpolated to any complex $n$ and how these interpolations are related to the Bethe algebra for the Deligne's category.
This is an ongoing project, joint with L. Rybnikov
We revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that supersymmetric Schwarzians can be systematically
obtained as certain projections of Maurer-Cartan forms of superconformal groups after imposing simple conditions on them.
We also present the supersymmetric Schwarzian actions, defined as the integrals of products of Cartan forms. In contrast with the previous attempts to obtain
the super-Schwarzians within nonlinear realizations technique, our set of constraints does not impose any restriction on the super-Schwarzians.
First, we consider the relationship between super Yangians and quantum loop superalgebras. We consider structures of tensor categories on analogs of the category $\mathfrak{O}$ for representations of the super Yangian $Y_{\hbar}(A(m,n))$ of the special linear Lie superalgebra and the quantum loop superalgebra $U_q(LA(m,n)) $, explore the relationship between them. The construction of an isomorphism in the category of Hopf superalgebras between completions of the super Yangian and the quantum loop superalgebra endowed with the so-called "Drinfeld" comultiplications is described. A theorem on the equivalence of the tensor categories of modules of the super Yangian and the quantum loop superalgebra is formulated, which strengthens the previous result. We also describe the relationship between Quasi-Triangular structures and Abelian difference equations, which are determined by the Abelian parts of universal $R$-matrices. Second, we define an affine super Yangian $Y_{\epsilon_1, \epsilon_2}(\tilde{sl}(m,n))$ for an arbitrary system of simple roots $\Pi$ of affine Kac-Moody superalgebra $\tilde{sl}(m,n)$. We introduce two type presentation of super Yangian, namely minimalistic and current presentation. We prove that this two presentations are equivalent. It is proved that the super Yangians of a quantum affine superalgebra $\tilde{sl}(m,n)$ defined by different simple root systems $\Pi$ and $\Pi_1$ are isomorphic as associative superalgebras. Some of these results were obtained in articles: V. A. Stukopin, Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra, Theoret. and Math. Phys., 204:3 (2020), 1227–1243., V. A. Stukopin, Quasi-triangular structures on the super Yangian and quantum loop superalgebra and difference equations, Theoret. and Math. Phys., 2022 (to appear). We also describe cosuperalgebra structures on affine Super Yangian.
The talk is dedicated to some variants of Regge-Gribov model, namely, to simplified one-dimensional model with pomeron and odderon field
\begin{multline}
H=-\left( \Phi^{+} \partial_y \Phi + \Psi^{+} \partial_y \Psi - L \right) = -\mu_P \Phi^{+}\Phi - \mu_O \Psi^{+} \Psi + \
i \lambda \left( \Phi^{+}\Phi^{+}\Phi + \Phi^{+}\Phi\Phi + 2 \Psi^{+} \Psi \Phi +2 \Phi^{+} \Psi^{+} \Psi - \Phi^{+} \Psi \Psi + \Psi^{+} \Psi^{+} \Phi \right)
\end{multline}
and three pomeron fields (of conformal spins 0,+2,-2)
\begin{multline}
H = - \mu_0 \Phi^+0 \Phi_0 - \mu_2 \left( \Phi^+{-2} \Phi_2 + \Phi^+2 \Phi{-2} \right) + \
i \lambda \left( \Phi^+0 \left( \Phi^2_0 + 2 \Phi_2 \Phi{-2} \right) + 2 \Phi^+2 \Phi{-2} \Phi_0 + 2 \Phi^+{-2} \Phi_2 \Phi_0 + \right. \
\left. \left( \Phi^{+ 2}_0 + 2 \Phi^+_2 \Phi^+{-2} \right) \Phi_0 + 2 \Phi^+2 \Phi^+_0 \Phi{-2} + 2 \Phi^+_{-2} \Phi^+_0 \Phi_2 \right)
\end{multline}
where transverse momenta dependence is neglected. These models, while not really being suited to quantitative purposes due to the possibility of transverse momenta being high in loops, they do provide qualitative results on whether inclusion of additional reggeons has any considerable effect on the behavior of propagators, while being quite significantly less cumbersome for calculations. Some analytical methods for further simplifications are provided, and then the results of performed numerical calculations are presented. Three-pomeron model is particularly interesting, since it can be transformed into two-pomeron model, thus all the calculations can be significantly simplified. Overall, the results obtained coincide with expectations, namely, inclusion of odderon increases propagators and inclusion of subdominant pomerons decreases them.
Within the framework of the model with quark-gluon strings (color flux tubes) as sources, the properties of the strongly intense variable Σ, which characterizes the correlations between the number of particles in two observation windows separated in rapidity, are studied. We use a Regge-like quasi-eikonal approach to find the distribution of strings in the transverse plane of pp-collision. This allows us to take into account string fusion processes leading to the formation of string clusters using a finite lattice (grid) in the impact parameter plane. Analytical calculations, supplemented by MC simulation, make it possible to find the dependences of the variable Σ both on the width of the observation windows and on the size of the gap between them depending on the initial energy and centrality of the collision.
We show that in pp collisions at LHC energies, string fusion effects leading to the formation of string clusters have a significant effect on the behavior of this variable. We demonstrate that the experimentally observed dependence of the strongly intensive variable Σ on the initial energy and centrality of pp collisions can be explained only in the presence of sources of different types, the role of which in our model is played by single strings and clusters formed by the fusion of several strings. It is also shown that a comparison of the results of our model with the preliminary experimental data of ALICE makes it possible to extract the parameters of clusters with different numbers of merged strings, in particular, to find their two-particle correlation functions.
The research was supported by the SPbSU project, No 93025435.
The properties of the multiplicity distribution of the charged particles, produced in pp collisions at high energy, can be studied using combinant analysis [1,2]. The modified combinants $C_j$ show the interplay between the neighboring probabilities, and satisfy the following recurrence relation:
$$
(N+1)P(N+1)=\sum\limits_{j=0}^{N}C_j P(N-j)
$$
The combinant analysis of the experimental data at LHC showed peculiar oscillatory behavior, that can not be to reproduce using standard distributions, usually applied to the $N_{ch}$ distributions (like Poisson and NBD), and in models [3]. It was showed that in the multi-pomeron exchange model the oscillation is sensitive to the multiplicity distribution from one emitting source and to the very first points of the overall pp multiplicity distribution [4].
In this report the combinants of the multiplicity distribution are considered in a Monte Carlo model with string fusion [5,6]. The charged particles spectra and distributions are obtained in the picture of quark-gluon strings, with the inclusion of string interaction in transverse plane, carried out in the
framework of local string fusion model with the introduction of the lattice in the impact parameter plane and taking into account the finite rapidity length of strings. The parameters of the model were fixed with experimental data on inelastic cross section and charged multiplicity at high energy range.
We studied the multiplicity distributions and combinants of different particle species and the influence of the string fusion and contribution of the short strings, as well as resonance production, on the combinants.
[1] G. Wilk and Z. Włodarczyk, J. Phys. G 44, 015002 (2017).
[2] G. Wilk and Z. Włodarczyk, Int. J. Mod. Phys. A 33, 1830008 (2018).
[3] E. Andronov, V. Kovalenko, A. Puchkov, Combinant analysis of multiplicity distributions in p+p interactions in multipomeron exchange model. LXXI International conference "NUCLEUS – 2021", St. Petersburg, 20-25 September 2021
[4] E. Andronov, V. Kovalenko, A. Putchkov, V. Vechernin, Multiplicity distributions and combinants in multi-pomeron exchange model. LXXII International conference "NUCLEUS – 2022", Moscow, 11-16 July 2022
[5] V. N. Kovalenko, Phys. Atom. Nucl. 76, 1189 (2013), arXiv:1211.6209 [hep-ph].
[6] V. Kovalenko, V. Vechernin, PoS (Baldin ISHEPP XXI) 077 (2012), arXiv:1212.2590 [nucl-th].
Recent works have explored interesting phenomena about quantum field theory in de Sitter space. One of the simple ways to estimate the behaviour of a system with matter in an external electric or gravitational field is to calculate the effective equation of motion for small perturbations of a background field in one-loop order. Further approximations allow us to introduce the notion of Debye mass for such perturbations. In this report, we will make a brief review of the work 'Debye mass in de Sitter space' (https://arxiv.org/abs/1711.11010), in which the effective Debye mass of a photon is calculated in scalar electrodynamics in de Sitter space. After that, we will discuss the prospect of calculating a similar quantity for a graviton in de Sitter space.
According to the Penrose process there might be particles with negative energy in the ergosphere of a rotating black hole. Later, it was shown that there might be also particles with zero energy but with not zero angular momentum. In this work we consider properties of such particles. In particular, we investigate the question about the inertial forces for such particles in equatorial plane $\theta=\frac{\pi}{2}$ and in general case. Also we consider the movement along the angle $\theta$. We show that inertial forces in the case of particles with zero energy in the equatorial plane is bigger than ones for particles with positive energy. It turns out that all forces in the zero energy case are proportional to the square of angular momentum $L^2$.
We consider a massive scalar field theory on static four-dimensional space-times with horizons. We study the near horizon behaviour of the quantum expectation values of the stress--energy tensor operator for the thermal states with arbitrary temperatures. It turns out that the dependence of the expectation values on the temperature and tensor structure of the stress--energy tensor are different from the usual ones in the Minkowski space-time. Moreover, for non--canonical temperatures these expectation values are divergent on the horizons. We also show that the Wightman functions have additional infrared peculiarities near the horizons.
Shapovalov elements $\theta_{\beta,m}$ in the classical or quantum universal enveloping algebra of the negative Borel subalgebra of a simple Lie algebra are parameterized by a positive root $\beta$ and a positive integer $m$. They relate the canonical generator of a reducible Verma module with highest vectors of its Verma submodules. We obtain a factorization of $\theta_{\beta,m}$ to a product of $\theta_{\beta,1}$, where the latter is calculated as a re-scaled matrix element of the inverse Shapovalov form
via a generalized Nigel-Moshinsky algorithm. This way we explicitly express all Shapovalov elements for a classical simple Lie algebra through the Cartan-Weyl basis. In the case of quantum groups, an analogous presentation is available through matrix elements of the universal R-matrix in a representation that goes to adjoint in the classical limit.
Since their invention over 30 years ago, quantum groups and their representations have been playing an important role in mathematical physics. To each semisimple Lie algebra g and a root of unity q,
one can associate the Lusztig’s “divided powers” quantum group at a root of unity. The category of its finite dimensional representations over complex numbers is non-semisimple and has a remarkable tensor subcategory, which leads in particular to the definition of the fusion category. It also changes the standard result about the multiplicity of a given finite dimensional representation in a tensor power of a standard representation. I will review some recent results in this area and discuss applications.
A convenient integral representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional fishnet field theory is obtained. This representation gives a possibility to evaluate exactly diagrams of the zig-zag series in special cases. In particular, we give a fairly simple proof of the Broadhurst-Kreimer conjecture about the values of zig-zag multi-loop two-point diagrams which make a significant contribution to the renormalization group beta-function in 4-dimensional phi^4 theory.
We present a basis of eigenvectors for the graph building operators of planar fishnet Feynman integrals in d-dimensions. The eigenvectors are constructed with a set of creation/annihilation operators that satisfy the corresponding Zamolodchikovs-Faddeev algebra. The spectral decomposition of a fishnet integral we achieved can be applied to the computation of Basso-Dixon integrals in higher dimensions.
In [1]-[5] we developed the theory of spinors on the basis of the superalgebraic representation. In it, spinor field operators are constructed from Grassmann densities in the momentum space and derivatives with respect to them. We have shown that generators of transformations that preserve the CAR algebra of spinor creation and annihilation operators are analogs of Dirac gamma matrices and can be constructed from Grassmann densities and their derivatives [1]-[3]. But, in contrast to the Dirac theory and its generalization within the framework of the second quantization method, in addition to the five usual Dirac gamma matrices, two additional gamma operators (basis Clifford vectors) appear in the theory of superalgebraic spinors [2]. In the matrix representation, they correspond to two additional gamma matrices. The generator of rotation in the plane of these vectors in the simplest case of four basis Grassmann densities is the operator of the electric charge of the spinor [4]. Using the superalgebraic representation, we were able to explicitly construct the state vector of the spinor vacuum [1], and also prove that the symmetries T and C transform this vacuum into an alternative one, which is why they cannot be exact symmetries of our Universe [4]-[5].
However, the main issue in the developed theory was the correspondence of the superalgebraic representation to the standard QFT. In this article, we have solved this issue. Instead of considering the superalgebraic representation of spinors, we have considered all possible transformations of the connected Lie group of spinor creation and annihilation operators that preserve their CAR algebra. We have shown that in the case of a four-component spinor, these transformations are generated by the seven gamma operators we obtained earlier, the corresponding Lorentz transformations, as well as the gauge transformations of the electromagnetic field associated with rotation in the plane of the sixth and seventh gamma operators (Clifford vectors). We discuss the limitations of no-go theorems on possible transformations of the Lie group of spinors, including in the presence of a multiplet of two spinors (an eight-component spinor) or more than four spacetime dimensions.
We discuss a limits on
a hidden sector models, which have been excluded
recently by NA64 fixed-target experiment at CERN SPS.
Namely, new experimental bounds on Dark Photon,
millicharged fermions and axion-like particles are
obtained from the missing energy signatures of
the electron beam incident on a lead target of NA64.
We also discuss prospects of NA64 to exclude light
dark matter with muon beam setup.
Following a nonperturbative formulation of strong-field QED developed in our earlier works, and using the Dirac model of the graphene, we construct a reduced QED_{3,2} to describe one species of the Dirac fermions in the graphene interacting with an external electric field and photons. On this base, we consider the photon emission in this model and construct closed formulas for the total probabilities. Using the derived formulas, we study probabilities for the photon emission by an electron and for the photon emission accompanying the vacuum instability in the quasiconstant electric field that acts in the graphene plane during the time interval T. We study angular and polarization distribution of the emission as well as emission characteristics in a high frequency approximation. We analyze conditions of the applicability of the presented calculations in possible experimental conditions. It allows one a laboratory verifying QED predictions for strong fields, in particular, real studying the Schwinger effect.
A phenomenological description of the process of particle production is explored on the example of the action of an ideal fluid with a variable number of particles. The Euler formalism is used because it allows to include the continuity equation in the matter action explicitly through a corresponding constraint. To pass to a model with a variable number of particles, it suffices to replace the aforementioned constraint with the particle creation law that contains the function $\Phi$ which depends on the invariants of the fields responsible for the creation process as a source. The left-hand side of the particle creation law multiplied by $\sqrt{|g|}$ is a conformal invariant so the term $\Phi\,\sqrt{|g|}$ is also a conformal invariant. Particles are born exclusively due to vacuum polarization, which is due to the influence of the gravitational field in the absence of classical external fields so $\Phi$ should depend solely on geometric invariants. The square of the Weyl tensor is the only option if we confine ourselves to invariants that are at most quadratic in the curvature tensor. This result is universal for Riemannian geometry regardless of the gravitational Lagrangian and it also takes into account the back reaction. Of particular physical interest is the situation where the possibility of particle production exists but is not realized. This is the so-called "pregnant vacuum", which is an example of a physical vacuum. It corresponds to the solution of the motion equations for which the number density and, as a consequence, the function $\Phi$ are zero. It is shown that in this case the matter that can potentially be born has a non-zero pressure. For spherically symmetric geometries in the absence of external fields the condition $\Phi=0$ leads to the fact that the two-dimensional scalar curvature $\widetilde{R}$ equals to 2. In this case, the momentum energy tensor obtained from the matter action is proportional to the Bach tensor and turns out to be zero. It is demonstrated that in general relativity in the absence of external fields there are no spherically symmetric vacuum solutions of the black hole type, which correspond to the physical vacuum for the action in question. The same is true for quadratic gravity if we restrict ourselves to static spacetimes with scalar curvature sufficiently quickly approaching a constant at spatial infinity. When an external scalar field is introduced into the particle creation law, the following combination is chosen: $\varphi \, \varphi^{;a}_{;a}-\frac{1}{6}\, \varphi^{2}\, R+\Lambda_0\, \varphi ^{4}$, since it gives a nontrivial motion equation and is conformally invariant when multiplied by $\sqrt{|g|}$. It is shown that in general relativity the physical vacuum in the spherically symmetric case cannot be the Schwarzschild-de Sitter metric even with the addition of a scalar field.
A generalization of Quark Model to construction of hadron spectroscopy is suggested. The proposed approach is applied to the case of light nonstrange mesons. By assumption, all such mesons above 1 GeV appear due to creation of constituent quark-antiquark pairs «inside» the pi or rho(omega) mesons. These spin-singlet or triplet pairs dictate the quantum numbers of formed resonance. Basing on the idea of renormalization group invariance of hadron masses, It is argued that the total energy of hadron constituents should be proportional to the hadron mass squared rather than linear mass. This leads to an effective mass counting scheme for meson spectrum. The given approach results in the linear Regge and radial Regge trajectories by construction. An experimental observation of these trajectories may thus serve as an evidence not for string but for multiquark structure of highly excited hadrons.
We investigate the free energy and entropy of the Gaussian massive scalar field theory in the static de Sitter space-time for arbitrary temperature.There are two types of contributions to the free energy: one is of the "area type" and can be attributed to the horizon, while the other is of the "volume type" and is associated with the interior of the space-time. The latter contribution in the odd-dimensional case in the limit of the week field (large mass or small Hubble constant) significantly depends on the temperature. Namely, for β<2π, the free energy behaves as Fbulkβ∼e−βm, while for β>2π it behaves as Fbulkβ∼e−2πm. We also show that even the leading UV contributions to the free energy significantly depend on the state of the theory, which is very unusual. We explain the origin and physical meaning of these observations. As the model example we consider the situation in the Rindler wedge of the flat space-time.