Resummation of infrared divergences in the free-energy of spin-two fields

TL;DR

This paper derives a closed-form expression for summing all infrared divergent contributions to the free-energy of a graviton gas, employing a gauge fixing that simplifies the graviton propagator, and extends this method to include interactions.

Contribution

It introduces a gauge fixing procedure that makes the graviton propagator traceless and transverse, enabling resummation of infrared divergences with interactions included.

Findings

Derived a closed-form expression for infrared divergences sum

Extended gauge fixing to interacting spin-two fields

Facilitated resummation of free-energy in graviton gases

Abstract

We derive a closed form expression for the sum of all the infrared divergent contributions to the free-energy of a gas of gravitons. An important ingredient of our calculation is the use of a gauge fixing procedure such that the graviton propagator becomes both traceless and transverse. This has been shown to be possible, in a previous work, using a general gauge fixing procedure, in the context of the lowest order expansion of the Einstein-Hilbert action, describing non-interacting spin two fields. In order to encompass the problems involving thermal loops, such as the resummation of the free-energy, in the present work, we have extended this procedure to the situations when the interactions are taken into account.