The long wavelength limit of hard thermal loop effective actions

TL;DR

This paper derives a simplified expression for the long wavelength limit of hard thermal loop effective actions in gravitational fields, highlighting its differences from static and Yang-Mills limits.

Contribution

It provides a novel closed-form expression for the long wavelength limit of hard thermal loop effective actions in external gravitational fields, independent of time derivatives.

Findings

Expression is a function of the metric only

Comparison with static limit shows key differences

Contrasts with limits in external Yang-Mills fields

Abstract

We derive a closed form expression for the long wavelength limit of the effective action for hard thermal loops in an external gravitational field. It is a function of the metric, independent of time derivatives. It is compared and contrasted with the static limit, and with the corresponding limits in an external Yang-Mills field.