Conformal Anomalies in Hydrodynamics

TL;DR

This work shows that conformal (trace) anomalies leave a non-dissipative imprint on the hydrodynamics of CFTs in even spacetime dimensions when studied on equilibrium curved backgrounds with a timelike Killing vector. By constructing a local anomalous action via a Wess-Zumino/dilaton approach and evaluating on Rindler space, the authors derive a universal, zero-derivative shift in the hydrodynamic pressure governed solely by the Euler density coefficient $a$, with Weyl-invariant contributions canceling on this background. The analysis recovers a two-dimensional Cardy-like relation and extends to higher dimensions, providing explicit expressions in $d=4$ and $d=6$ that tie the pressure to the Euler term and a dimension-dependent coefficient $n$, while showing the pressure can retain coupling dependence through invariant terms. These results clarify how trace anomalies influence equilibrium hydro, connect to the dilaton/Wess-Zumino framework, and offer a concrete route to compute anomaly-induced transport in holographic and strongly coupled CFT contexts.

Abstract

We study the effect of conformal anomalies on the hydrodynamic description of conformal field theories in even spacetime dimensions. We consider equilibrium curved backgrounds characterized by a time-like Killing vector and construct a local low energy effective action that captures the conformal anomalies. Using as a special background the Rindler spacetime we derive a formula for the anomaly effect on the hydrodynamic pressure. We find that this anomalous effect is only due to the Euler central charge.