Universality of Transport Properties in Equilibrium, the Goldstone Theorem, and Chiral Anomaly

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 nonvanishing 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 a background magnetic field in $3+1$ dimensions.