Two dimensional hydrodynamics with gauge and gravitational anomalies

TL;DR

This work addresses how gauge and gravitational anomalies modify hydrodynamics in $1+1$ dimensions by deriving exact, non-perturbative constitutive relations for the stress tensor $T_{ab}$ and current $J^a$ from covariant anomalies and the Polyakov effective action. It treats both non-chiral and chiral theories, obtaining closed-form expressions that do not rely on gradient expansion and, in the chiral case, cast the results in an ideal chiral fluid form using a chiral velocity $u^{(c)}_a$. A key finding is that, in the chargeless limit, the exact results reproduce gradient-expansion results with a specific constant $\bar{C}=\pi/12$, while the formalism also incorporates gauge fields in a manner unavailable in standard gradient approaches. The work clarifies the interplay between covariant and consistent anomalies in two dimensions and provides a robust framework for exact anomalous hydrodynamics with charge and gravity coupling, with potential implications for related low-dimensional systems and holographic contexts.

Abstract

We present a new approach to discuss two dimensional chiral and non-chiral hydrodynamics with gauge and gravitational anomalies. Exact constitutive relations for the stress tensor and charge current are obtained. For the chiral theory, the constitutive relations may be put in the ideal (chiral) fluid form whereas the constitutive relations corresponding to non-chiral case do not take the ideal fluid form. The constitutive relations in the presence of both gravity and gauge sectors are new. These expressions, in the absence of the gauge sector, reproduce the results obtained in the gradient expansion approach.