General structure of the graviton self-energy

TL;DR

This paper investigates the structure of the graviton self-energy at finite temperature, revealing gauge invariance constraints that relate multiple structure functions and verifying these relations at one-loop order.

Contribution

It identifies three non-linear relations among the fourteen structure functions of the thermal graviton self-energy due to gauge invariance, valid to all orders.

Findings

Gauge invariance imposes three non-linear relations among structure functions.

Constraints are verified explicitly at one-loop order in linear gauges.

Relations hold in the absence of tadpoles, ensuring consistent thermal graviton self-energy.

Abstract

The graviton self-energy at finite temperature depends on fourteen structure functions. We show that, in the absence of tadpoles, the gauge invariance of the effective action imposes three non-linear relations among these functions. The consequences of such constraints, which must be satisfied by the thermal graviton self-energy to all orders, are explicitly verified in general linear gauges to one loop order.