Second order transport from anomalies

TL;DR

This work investigates parity-odd transport in a relativistic, non-conformal charged fluid with a single anomalous current at second order in derivatives. It combines the equilibrium partition function method with Kubo-formula calculations to constrain seven parity-odd coefficients in terms of the quantum anomaly and hydrodynamic data, while deriving three anomaly-related relations among the remaining coefficients. The results yield explicit expressions for the second-order coefficients, and a holographic check using a Reissner–Nordström AdS5 background confirms the relation between the first coefficient and the gauge anomaly and shows a vanishing $\Phi_{12}$ for ${\cal N}=4$ SYM. The analysis also reveals chiral shear-wave dispersion modifications and connects to three-point functions in the general setting, suggesting further extensions to all coefficients and holographic comparisons.

Abstract

We study parity odd transport at second order in derivative expansion for a non-conformal charged fluid. We see that there are 27 parity odd transport coefficients, of which 12 are non-vanishing in equilibrium. We use the equilibrium partition function method to express 7 of these in terms of the anomaly, shear viscosity, charge diffusivity and thermodynamic functions. The remaining 5 are constrained by 3 relations which also involve the anomaly. We derive Kubo formulae for 2 of the transport coefficients and show these agree with that derived from the equilibrium partition function.