Supersymmetric field theory for beginners
I.L. Buchbinder (TSPU, Tomsk, Russia)
Lecture 1 Lecture 2
Abstract
This lecture course is devoted to an elementary introduction to the basic concepts of N = 1 supersymmetric classical field theory. It is assumed that the listeners have never studied this subject and this is their first acquaintance with supersymmetry. The course is intended for students familiar with the basic elements of Lie group theory and classical relativistic field theory.
Contents
Lecture 1. Basic idea of supersymmetry. Lorentz and Poincare groups. Two- component spinors. Lie algebra of the Poincare group.
Lecture 2. Super extension of the Poincare algebra. Supercharges. Anticommuting variables. Superspace and superfield. Chiral superfields.
Lecture 3. Superfield Lagrangians. Wess-Zumino model. Supersymmetric Yang-Mills theory.
Literature:
- I.L. Buchbinder, S.M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity or a Walk Through Superspace, IOP Publishing, Bristol and Philadelphia, 1998.
Field theory in AdS Space (Higher Spins)
Ruben Manvelyan (Yerevan Physics Institute,Armenia)
-
Geometry of AdSD. Geodesics, trajectories, and one-parameter subgroups
-
Conformally coupled massless scalar in general gravitational background and restriction to AdS case. The Cauchy problem and the antipodal map.
-
Fronsdal Equation . General setup for higher spin equation of motion.
Geometric Quantization: sketch of the unfinished story
N.A.Tyurin (BLTP JINR, Dubna, Russia)
Geometric Quantization of Classical Mechanical systems with compact phase space was in the focus of the investigations both in geometry and in mathematical physics. In contrast with, say, deformation quantization, Geometrical approach is based on the entire geometry of the phase space. In the 60s, the famous Souriou-Kostant method was proposed, which was called geometric quantization. In brief notes, I will present the basic facts of symplectic geometry (= phase space geometry) and review how a classical mechanical system can be reconstructed from a finite-dimensional Hilbert space.
Introduction to twistors and supertwistors
S. Fedoruk (BLTP JINR, Dubna, Russia) Lectures 1 and 2.pdf
Lecture 1.
Conformal symmetry and twistors. Twistor space.
Penrose twistor transform and twistor formulation of massless particles.
Field twistor transform.
Twistorial description of higher spin particle.
Lecture 2.
Bitwistor formulation of massive particles and massless infinite spin
particles.
Conformal supersymmetry and supertwistors.
Twistor description of massless superparticles.
Factorized Scattering Theory and the Bethe Ansatz
Gleb Arutyunov (Hamburg University)
Abstract
In these lectures we treat the elemental aspects of quantum integrable
models related to Factorized Scattering Theory and the Bethe Ansatz.
Factorized Scattering Theory
1.Classical scattering and integrability
2.Conservation laws and the Bethe wave function
3.S-matrix
Coordinate Bethe Ansatz
1.Periodicity condition for the Bethe wave function
2.Incarnations of the Lieb-Liniger model
3.Spin chain representation of permutation modules
4.Generalised Bethe hypothesis
Transfer Matrix Method
1.Transfer matrix
2.Diagonalisation of the transfer matrix by Lieb's method
3.Algebraic Bethe Ansatz
4.Nested Bethe Ansatz
Recommended literature:
-
C.N. Yang, Some exact results for the many body problems in one
dimension with
repulsive delta function interaction, Phys. Rev. Lett., 19:1312--1314,
1967. -
C.N. Yang, S matrix for the one-dimensional N body problem with
repulsive or
attractive delta function interaction, Phys. Rev., 168:1920--1923, 1968. -
A.B. Zamolodchikov and Al.B. Zamolodchikov,
Factorized S Matrices in Two-Dimensions as the Exact Solutions of
Certain Relativistic Quantum Field Models.
Annals Phys., 120:253--291, 1979. -
L. D. Faddeev, How Algebraic Bethe Ansatz works for integrable model,
Les-Houches lectures, arXiv:hep-th/9605187. -
M. Gaudin, The Bethe Wavefunction, Translated from French original ``La
fonction d'onde de Bethe' (1983) by J.-S. Caux, Cambridge University
Press, 2014. -
G. Arutyunov, Elements of classical and quantum integrable systems,
Springer, 2019.
Supersymmetric quantum mechanics
S. Sidorov (BLTP JINR, Dubna, Russia) Lecture 1.pdf Lecture 2.pdf
Abstract
Supersymmetric quantum mechanics is the simplest d=1 supersymmetric field
theory which displays salient features of higher-dimensional supersymmetric
theories via dimensional reduction. I will consider N=4, d=1 supersymmetry
that is related to N=1, d=4 supersymmetry (Lectures of I.L. Buchbinder).
Lecture 1. Introduction. N=4, d=1 supersymmetry. Scalar, сhiral and
harmonic superfields. Superfield Lagrangians.
Lecture 2. Deformed (Weak) supersymmetry. Model of harmonic oscillator.
Quantization.
Seminar:
Maneh Avetisyan
A. I. Alikhanian National Science Laboratory, Yerevan Physics Institute
Vogel’s universality and its applications
(based on the P.h.D. thesis)
Students' talks
Prokopii Anempodistov (MIPT), Infrared loop corrections in the Friedmann Universe
Kseniya Arhipova (Uni.Dubna & BLTP), Formation of trapped surfaces in asymptotically curved spacetime
Lev Astrakhantsev (MIPT & ITEP), Non-Abelian Fermionic T-duality in supergravity
Alexandra Budekhina (Tomsk SPU), One-loop divergences in 4D, N = 2 harmonic superfield sigma-model .pdf
Ivan Burenev (PDMI RAS), R-matrix of the five-vertex model
Mher Davtyan (IRE NAS Armenia), The role of light polarization and related effects in Maxwell fish-eye refractive profile
Dusan Djordjevic (Inst. of Physics, Belgrade), 4D Gravity from 5D noncommutative Chern-Simons theory
Olesya Geytota (Uni.Dubna & BLTP), Energy spectrum of a pulsating string in a Kerr anti-de Sitter black hole
Kirill Gubarev (MIPT), Generalized 11 dimensional supergravity .pdf
Ilija Ivanisevic (Inst. of Physics, Belgrade), Courant algebroids in bosonic string theory
Erik Khastyan (Yerevan Physics Inst.), Non-compact complex projective spaces as a phase space of integrable systems: supersymmetric extensions
Nikita Kolganov (MIPT & ITEP), Chern-Simons TQFT and topological quantum computations
Jeremy Mann (DESY Hamburg), Multipoint conformal blocks from Gaudin integrable systems [Zoom] .pdf
Mustafa Mullahasanoglu (Boğaziçi University), Lens partition function and integrability properties in statistical mechanics [Zoom] .pdf
Tijana Radenkovic (Inst. of Physics, Belgrade), Higher gauge theories based on 3-groups
Daniil Sarafannikov (SPbU), Limit form of Young diagrams for an ensemble of Kravchuk q-polynomials
Leonid Shumilov (HSE SPB),Mellin–Barnes transformation for two-loop master-diagram
Dmitrii Trunin (MIPT), Particle creation in a toy O(N) model .pdf
Elizaveta Trunina (MIPT), Identification of discrete Painleve equations .pdf
Marina Usova (Uni.Dubna & BLTP), Holographic RG flows in 3d supergravity
Nikita Zaigraev (MIPT & JINR), N=2 supersymmetric higher spins
