Thermodynamics, gravitational anomalies and cones

TL;DR

This paper investigates how gravitational anomalies influence hydrodynamic coefficients through Euclidean partition functions on cones, revealing lower-order effects of anomalies in various dimensions.

Contribution

It demonstrates that gravitational anomalies produce parity-violating terms in hydrodynamics, affecting coefficients at unexpectedly low orders in the gradient expansion.

Findings

Anomalies generate a 'Casimir momentum' observable.

In 1+1 dimensions, anomalies affect zeroth-order coefficients.

In 3+1 dimensions, mixed anomalies influence first-order coefficients.

Abstract

By studying the Euclidean partition function on a cone, we argue that pure and mixed gravitational anomalies generate a "Casimir momentum" which manifests itself as parity violating coefficients in the hydrodynamic stress tensor and charge current. The coefficients generated by these anomalies enter at a lower order in the hydrodynamic gradient expansion than would be naively expected. In 1+1 dimensions, the gravitational anomaly affects coefficients at zeroth order in the gradient expansion. The mixed anomaly in 3+1 dimensions controls the value of coefficients at first order in the gradient expansion.