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Anomalous gravitational TTT vertex, temperature inhomogeneity, and pressure anisotropy. (English) Zbl 1435.81200
Summary: 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.
MSC:
81T50 Anomalies in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
81V10 Electromagnetic interaction; quantum electrodynamics
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