Hydrodynamics in 1+1 dimensions with gravitational anomalies

TL;DR

Problem: understand how gravitational anomalies modify hydrodynamics in $1+1$ dimensions. Method: compute a local anomalous partition function term at second derivative order in a time-independent background and derive the covariant energy-momentum tensor via a Bardeen shift, avoiding entropy-based arguments. Contributions: derive parity-odd corrections to the current and energy-momentum tensor in the Landau frame, including a novel second-order current term, and show how the zero-order gauge anomaly is incorporated. Significance: establishes a concrete, entropy-free framework for anomaly-induced transport in low-dimensional relativistic fluids and sets the stage for mixed gauge-gravitational effects in higher dimensions.

Abstract

The constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at second derivative order. This partition function is then used to compute the parity-violating part of the covariant energy-momentum tensor and the transport coefficients.