Comparative study of loop contributions in AdS and dS

TL;DR

This paper compares loop contributions in Anti-de Sitter and de Sitter spaces, revealing that unlike de Sitter, Anti-de Sitter does not exhibit large IR effects or divergences at one-loop level, even for massless scalars.

Contribution

It demonstrates the absence of large IR loop effects in Anti-de Sitter space, contrasting with de Sitter space, and clarifies misconceptions from naive analytic continuation.

Findings

No large IR effects in one-loop two-point functions in Poincare AdS

No IR divergences in global AdS for massless fields

Contrasts with IR behavior in de Sitter space

Abstract

The generic feature of non-conformal fields in Poincare patch of de Sitter space is the presence of large IR loop corrections even for massive fields. Moreover, in global de Sitter there are loop IR divergences for the massive fields. Naive analytic continuation from de Sitter to Anti-de-Sitter might lead one to conclude that something similar should happen in the latter space as well. However, we show that there are no large IR effects in the one-loop two-point functions in the Poincare patch of Anti-de-Sitter space even for the zero mass minimally coupled scalar fields. As well there are neither large IR effects nor IR divergences in global Anti-de-Sitter space even for the zero mass.