Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly

TL;DR

This paper explores how the universality of transport properties in systems with chiral charges relates to the chiral anomaly, linking gapless modes and nonrenormalization of anomalies through a new current formula.

Contribution

It introduces a novel formula connecting currents to anomalous commutators, demonstrating the universal conductance arising from anomaly nonrenormalization.

Findings

Universality of conductance is linked to anomaly nonrenormalization.

A new formula expresses currents via anomalous commutators.

Transport properties in specific models are analyzed.

Abstract

We study transport in a class of physical systems possessing two conserved chiral charges. We describe a relation between universality of transport properties of such systems and the chiral anomaly. We show that the non-vanishing of a current expectation value implies the presence of gapless modes, in analogy to the Goldstone theorem. Our main tool is a new formula expressing currents in terms of anomalous commutators. Universality of conductance arises as a natural consequence of the nonrenormalization of anomalies. To illustrate our formalism we examine transport properties of a quantum wire in (1+1) dimensions and of massless QED in background magnetic field in (3+1) dimensions.