Higher-form symmetries, anomalous magnetohydrodynamics, and holography

TL;DR

This work develops a holographic framework for anomalous magnetohydrodynamics governed by a dynamical axial current with a chiral anomaly, recast in terms of a 2-form current associated with magnetic flux conservation. By constructing a bulk theory with a massless 2-form and a (non-gauge) vector field, and performing a bulk Poincaré duality, the authors engineer a universal description that yields the boundary anomaly $\partial_\mu j_A^\mu = k\epsilon_{\mu\nu\rho\sigma} J^{\mu\nu} J^{\rho\sigma}$ and allows computation of the axial-charge susceptibility $\chi$ and relaxation rate $\Gamma_A$ as functions of temperature $T$ and magnetic field $B$. In the hydrodynamic, small-$B$ regime the results reproduce the expected $\Gamma_A \propto B^2$, in agreement with simple chiral MHD arguments, while at large $B$ the relaxation rate exhibits nontrivial UV-sensitive behavior not captured by low-energy hydrodynamics. Comparisons with lattice simulations show qualitative consistency in the quadratic-$B$ scaling but indicate important short-distance physics, motivating further studies of UV completions and hydrodynamic effective theories for anomalous magnetohydrodynamics.

Abstract

In $U(1)$ Abelian gauge theory coupled to fermions, the non-conservation of the axial current due to the chiral anomaly is given by a dynamical operator $F_{μν} \tilde{F}^{μν}$ constructed from the field-strength tensor. We attempt to describe this physics in a universal manner by casting this operator in terms of the 2-form current for the 1-form symmetry associated with magnetic flux conservation. We construct a holographic dual with this symmetry breaking pattern and study some aspects of finite temperature anomalous magnetohydrodynamics. We explicitly calculate the charge susceptibility and the axial charge relaxation rate as a function of temperature and magnetic field and compare to recent lattice results. At small magnetic fields we find agreement with elementary hydrodynamics weakly coupled to an electrodynamic sector, but we find deviations at larger fields.

Figures (3)

• Figure 1: $\chi/T^2$ as a function of $kb/T^2$
• Figure 2: $\Gamma_A$ vs $b$ with $k=0.0375$ and $r_h=1$ (blue curve is numerics, orange curve is quadratic fit)
• Figure 3: $\Gamma^{\mathrm{improved}}_{A}$ from \ref{['Gamma5_1']} (i.e. chiral MHD with weakly coupled electrodynamics) as a function of $b$ with $k=0.0375$ and $r_h=1$; note it does not capture the non-trivial dependence on $b$ seen in the numerical results of Figure \ref{['qnml0_1']}