Triangle Anomalies, Thermodynamics, and Hydrodynamics

TL;DR

This paper investigates how anomalies affect the thermodynamics and hydrodynamics of 3+1-dimensional fluids, deriving relations for conductivities and ensuring consistency within the theoretical framework.

Contribution

It introduces a method using Ward identities to derive relations between correlation functions and fixes anomaly-induced conductivities in hydrodynamics.

Findings

Derived differential equations relating correlation functions.

Obtained expressions for chiral magnetic conductivity.

Showed hydrodynamic consistency fixes anomaly-induced conductivities.

Abstract

We consider 3+1-dimensional fluids with U(1)^3 anomalies. We use Ward identities to constrain low-momentum Euclidean correlation functions and obtain differential equations that relate two and three-point functions. The solution to those equations yields, among other things, the chiral magnetic conductivity. We then compute zero-frequency functions in hydrodynamics and show that the consistency of the hydrodynamic theory also fixes the anomaly-induced conductivities.