Anomalous gravitational TTT vertex, temperature inhomogeneity, and pressure anisotropy

M.N Chernodub,Claudio Corianò,Matteo Maria Maglio

doi:10.1016/j.physletb.2020.135236

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 Tμν. 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.

Highlights

A physical system is defined to be scale invariant at the classical level when all the parameters of the system are dimensionless quantities
The chiral magnetic effect is responsible for the effect of negative magnetoresistivity, which has been experimentally observed in Weyl and Dirac semimetals
In this work we have shown that the conformal anomaly leads to a qualitatively new effect

Summary

Introduction

A physical system is defined to be scale invariant at the classical level when all the parameters of the system are dimensionless quantities. The chiral magnetic effect is responsible for the effect of negative magnetoresistivity, which has been experimentally observed in Weyl and Dirac semimetals Another example in the same theory is given by the AAA diagram, with three axial-vector currents (A), which is responsible for the non-conservation of the axial charge in the background of an axial-vector gauge field. The AAA vertex is responsible for a variant of the chiral magnetic effect which generates the axial current in the background of the axial magnetic field at nonzero chiral chemical potential Such chiral effects are exotic properties of the fundamental interactions in the high energy physics domain, they may readily appear in effective theories of strained Weyl semimetals.

The flat-space case

Anomaly action

Scale electromagnetic effects

The TTT vertex

Conclusions