Exact results in two dimensional chiral hydrodynamics with gravitational anomalies

TL;DR

This work provides an exact, non-perturbative constitutive relation for two-dimensional chiral hydrodynamics with both diffeomorphism and trace (gravitational) anomalies, leveraging the unique features of 1+1D to avoid derivative expansions. It reveals a one-parameter family of solutions and shows that a specific parameter choice reproduces gradients-based results, while revealing a canonical ideal-chiral-fluid form governed by chirality. By mapping the anomalous stress tensor to an ideal chiral-fluid structure with modified energy density and pressure, the authors highlight how chirality imposes a distinct, universal tensor form in 2D. The results offer a robust framework for exact hydrodynamics in low dimensions and point to extensions to charged or nonchiral cases and to higher-dimensional generalizations.>

Abstract

An exact formulation of two dimensional chiral hydrodynamics with diffeomorphism and conformal anomalies is provided. The constitutive relation involving the stress tensor is computed. It reveals a one parameter class of solutions which is a new result. For a particular value of this parameter, the results found in the gradient expansion scheme are reproduced. Moreover, the constitutive relation is analogous to the corresponding relation for an ideal fluid, appropriately modified to include the chirality property, which has also been derived here.