Hard Thermal Loops, Weak Gravitational Fields and The Quark Gluon Energy Momentum Tensor

TL;DR

This paper develops a method to derive the hard thermal loop effective action for massless thermal SU(N) QCD in weak gravitational fields, enabling calculation of the quark-gluon plasma energy-momentum tensor.

Contribution

It introduces an auxiliary field approach to improve the derivation of the effective action, extending it beyond previous partial results to first order in graviton coupling.

Findings

Successfully calculated the symmetric traceless quark-gluon plasma energy-momentum tensor.

Clarified the conserved currents and charges associated with the energy-momentum tensor.

Identified limitations of previous derivations in the context of weak gravitational fields.

Abstract

We use an auxiliary field construction to discuss the hard thermal loop effective action associated with massless thermal SU(N) QCD interacting with a weak gravitational field. It is demonstrated that the previous attempt to derive this effective action has only been partially successful and that it is presently only known to first order in the graviton coupling constant. This is still sufficient to enable a calculation of a symmetric traceless quark gluon plasma energy momentum tensor. Finally, we comment on the conserved currents and charges of the derived energy momentum tensor.