Anomaly/Transport in an Ideal Weyl gas

TL;DR

This work builds a microscopic, adiabatic spectral-flow framework for anomaly-induced transport in an ideal Weyl gas across arbitrary even spacetime dimensions. By introducing a chiral spectral current $J^\mu_q(x,E_p)$ and enforcing adiabaticity, it derives a closed-form expression for state flow and shows that the anomaly-induced Gibbs current can be obtained from the anomaly polynomial via a simple substitution rule, $F\to \mu$ and $p_1(R)\to -T^2$, with higher Pontryagin classes absent from transport. The central result generalizes the 2d case to arbitrary $d=2n$ and provides a generating-function approach to relate anomaly data to transport coefficients in a dimension-agnostic way, offering a robust, non-dissipative mechanism for anomaly-related transport and potential connections to holography and non-equilibrium dynamics. The findings illuminate how gravitational and gauge anomalies shape finite-temperature transport in Weyl systems and suggest concrete paths to test the framework in interacting theories and curved spacetimes.

Abstract

We study some of the transport processes which are specific to an ideal gas of relativistic Weyl fermions and relate the corresponding transport coefficients to various anomaly coefficients of the system. We propose that these transport processes can be thought of as arising from the continuous injection of chiral states and their subsequent adiabatic flow driven by vorticity. This in turn leads to an elegant expression relating the anomaly induced transport coefficients to the anomaly polynomial of the Ideal Weyl gas.