# Anomalous Gravitational TTT Vertex, Temperature Inhomogeneity, and Pressure Anisotropy

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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-02349847
Contributor : Maxim Chernodub <>
Submitted on : Tuesday, November 5, 2019 - 6:51:02 PM
Last modification on : Wednesday, November 6, 2019 - 1:46:38 AM

### Citation

M. N. Chernodub, Claudio Corianò, Matteo Maria Maglio. Anomalous Gravitational TTT Vertex, Temperature Inhomogeneity, and Pressure Anisotropy. 2019. ⟨hal-02349847⟩

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