IR Renormalisation of General Effective Actions and Hawking Flux in 2D Gravity Theories

TL;DR

This paper investigates the infrared divergences in 2D effective actions using Covariant Perturbation Theory, proposing a renormalisation scheme that isolates divergences and relates to coupling with an external classical field.

Contribution

It introduces a summation scheme that isolates divergences in 2D effective actions, linking the renormalisation process to coupling with a classical external field.

Findings

Divergences are regularised by a mass parameter.

A summation scheme isolates divergences into a single term.

The finite part is equivalent to coupling with a classical external field.

Abstract

The infrared problem of the effective action in 2D is discussed in the framework of the Covariant Perturbation Theory. The divergences are regularised by a mass and the leading term is evaluated up to the third order of perturbation theory. A summation scheme is proposed which isolates the divergences from the finite part of the series and results in a single term. The latter turns out to be equivalent to the coupling to a certain classical external field. This suggests a renormalisation by factorisation.