Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory

TL;DR

This paper uses lattice simulations and higher-form symmetry to analyze transport properties in a finite-temperature Abelian gauge theory, confirming effective field theory predictions and clarifying the concept of conductivity at strong coupling.

Contribution

It introduces a higher-form symmetry framework to study chiral transport and plasma relaxation in lattice gauge theories, providing new insights into resistivity and conductivity at strong coupling.

Findings

Transport coefficients match effective field theory predictions.

Higher-form symmetry clarifies plasma relaxation mechanisms.

Resistivity remains well-defined at strong coupling.

Abstract

We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma -- defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD -- remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.