Thermal one- and two-graviton Green's functions in the temporal gauge

TL;DR

This paper calculates thermal graviton Green's functions in the temporal gauge, analyzing high-temperature behavior and verifying gauge independence, Ward identities, and the structure of subleading contributions in a rigorous manner.

Contribution

It introduces an ambiguity-free technique for computing thermal graviton Green's functions in the temporal gauge and verifies key identities and behaviors at high temperature.

Findings

Leading T^4 contributions are gauge independent.

Subleading T^2 and log(T) terms are explicitly computed and verified.

Extra prescription pole terms do not affect the main thermal contributions.

Abstract

The thermal one- and two-graviton Green's function are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading T^4 as well as the subleading T^2 and log(T) contributions to the graviton self-energy. The gauge fixing independence of the leading T^4 terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the 't Hooft identities for the subleading T^2 terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading T^2 contributions.