Chiral conductivities and effective field theory

We construct the three-dimensional effective field theory which reproduces low-momentum static correlation functions in four-dimensional quantum field theories with U(1) axial anomalies and a dynamical vector gauge field, in thermal equilibrium. We compute radiative corrections to parity-violating chiral conductivities, to leading order in the effective theory. All of the anomaly-induced transport is susceptible to radiative corrections, except for certain two-point functions which are required by symmetry to vanish.