Anomalous Gravitational TTT Vertex, Temperature Inhomogeneity, and Pressure Anisotropy

TL;DR

This paper explores how the conformal anomaly in curved spacetime causes a pressure anisotropy in a gas of charged massless particles due to temperature inhomogeneity, offering potential experimental insights into gravitational anomalies.

Contribution

It demonstrates that the $TTT$ vertex links temperature inhomogeneity to pressure anisotropy, providing a novel way to access the gravitational coefficient $b$ associated with the conformal anomaly.

Findings

Pressure anisotropy arises from temperature inhomogeneity via the $TTT$ vertex.

The effect is estimated to be small but detectable in Dirac semimetals and quark-gluon plasma.

The signature offers a potential experimental probe of gravitational anomalies.

Abstract

The conformal anomaly in curved spacetime generates a nontrivial anomalous vertex, given by the three-point correlation function $TTT$ of the energy-momentum tensor $T^{\mu\nu}$. We show that a temperature inhomogeneity in a gas of charged massless particles generates, via the $TTT$ vertex, a pressure anisotropy with respect to the axis of the temperature variation. This very particular signature may provide an experimental access to the elusive gravitational coefficient $b$ which determines the anomaly contribution of the Weyl tensor to the trace of the energy-momentum tensor in curved spacetime. We present an estimate of the pressure anisotropy both for fermionic quasiparticles in the solid-state environment of Dirac semimetals as well as for a quark-gluon plasma in relativistic heavy-ion collisions. In both cases, the pressure anisotropy is small compared to the mean thermal pressure.