Speaker
Description
We performed a two-loop field-theoretic analysis of incompressible, helical magnetohydrodynamics (MHD) in a fully developed, statistically stationary turbulent state. A distinctive feature of turbulence in helical media is the emergence, within the loop expansion of the magnetic response function, of an infrared-relevant, mass-like contribution. Physically, this term corresponds to a perturbation of the Joule dissipation proportional to the current helicity, ${\bf \nabla}\times{\bf b}$ (with ${\bf b}$ the magnetic field), and its presence destabilizes the trivial vacuum $\langle {\bf b} \rangle = 0$, thereby rendering the entire system unstable. We identify two stabilization mechanisms: (i) the induction equation governing the magnetic field can be augmented by an external mass-like parameter that exactly cancels the dangerous loop correction, thereby defining a kinematic regime; (ii) alternatively, the system may undergo spontaneous breaking of rotational symmetry, selecting a new vacuum endowed with a nonvanishing large-scale mean field $\langle {\bf b} \rangle = {\bf B}$—a turbulent dynamo regime. Physically, the (large-scale) dynamo regime is the state that typically emerges in MHD systems after sufficient time. By contrast, the kinematic regime provides an approximation valid when the emergent ${\bf B}$ remains relatively small. Our study focuses primarily on the dynamo regime, which is widely understood to underlie the generation of magnetic fields in astrophysical objects. We demonstrate that the emergence of an anomalous mean magnetic field is sufficient to stabilize the system, and we provide a two-loop determination of its amplitude. Our analysis shows that the appearance of ${\bf B}$ induces Goldstone-type modifications of the Alfvén modes and generates additional anisotropic structures. For turbulent spectra in the dynamo regime, we compute the two-loop contribution to the magnetic-field anomalous dimension $\gamma_b$. We find that the emergent mean field steepens the magnetic-energy spectrum to $\sim k^{-11/3+2\gamma_{b\star}}$ (with $\gamma_{b\star}=-0.1039-0.4202,\rho^2$ for $|\rho|\le 1$, where $\rho$ quantifies helicity and $\gamma_{b\star}$ denotes $\gamma_b$ evaluated at the Kolmogorov fixed point), in contrast to the Kolmogorov velocity spectrum $\sim k^{-11/3}$; hence the equipartition characteristic of the kinematic regime is violated. Moreover, the dependence of $\gamma_b$ on the mirror-symmetry-breaking parameter $\rho$—which first appears only at two loops—reveals an exceptionally strong sensitivity of the energy cascade to the degree of helicity.
