Anomalous transport at weak coupling

TL;DR

This paper calculates how chiral particles contribute to parity odd transport properties at finite temperature, revealing a breakdown of anomaly-transport relations for gravitinos and introducing a new method for angular integral evaluation.

Contribution

It provides a detailed one-loop analysis of parity odd transport coefficients for various chiral theories and introduces a simplified angular integral evaluation method.

Findings

Parity odd transport coefficients match anomaly predictions for fermions and bosons.

Relation between gravitational anomalies and transport breaks down for gravitinos.

Charge diffusion speed in 2D Weyl gas is half the speed of light.

Abstract

We evaluate the contribution of chiral fermions in $d=2, 4, 6$, chiral bosons, a chiral gravitino like theory in $d=2$ and chiral gravitinos in $d=6$ to all the leading parity odd transport coefficients at one loop. This is done by using finite temperature field theory to evaluate the relevant Kubo formulae. For chiral fermions and chiral bosons the relation between the parity odd transport coefficient and the microscopic anomalies including gravitational anomalies agree with that found by using the general methods of hydrodynamics and the argument involving the consistency of the Euclidean vacuum. For the gravitino like theory in $d=2$ and chiral gravitinos in $d=6$, we show that relation between the pure gravitational anomaly and parity odd transport breaks down. From the perturbative calculation we clearly identify the terms that contribute to the anomaly polynomial, but not to the transport coefficient for gravitinos. We also develop a simple method for evaluating the angular integrals in the one loop diagrams involved in the Kubo formulae. Finally we show that charge diffusion mode of an ideal 2 dimensional Weyl gas in the presence of a finite chemical potential acquires a speed, which is equal to half the speed of light.