Loops in Anti-de Sitter Space

TL;DR

This paper derives analytic results for one- and two-loop correlation functions of scalar fields in four-dimensional Euclidean anti-de Sitter space, offering insights into boundary behavior and renormalization without relying on conformal field theory assumptions.

Contribution

It provides the first explicit analytic calculations of loop amplitudes in AdS space without using conformal field theory techniques.

Findings

Analytic one-loop four-point amplitude in AdS

Two-loop expressions for two-point functions

Boundary correlation exponents inform renormalization

Abstract

We obtain analytic results for the four-point amplitude, at one loop, of an interacting scalar field theory in four-dimensional, Euclidean anti-de Sitter space without exerting any conformal field theory knowledge. For the two-point function, we provide analytic expressions up to two loops. In addition, we argue that the critical exponents of correlation functions near the conformal boundary of anti-de Sitter space provide the necessary data for the renormalization conditions, thus replacing the usual on-shell condition.