Weyl geometry, anti-De Sitter space, and $\Phi^4$-theory

TL;DR

This paper investigates quantum fluctuations of the metric in four-dimensional anti-De Sitter space using Gaussian approximation, addressing infrared divergences through mass renormalization linked to the cosmological constant.

Contribution

It constructs the generating functional for correlation functions of a self-interacting scalar field in AdS space and demonstrates how mass renormalization resolves infrared divergences.

Findings

Infrared divergence is cured by mass renormalization.

Cosmological constant provides the mass renormalization.

Renormalization affects the coupling constant of the field theory.

Abstract

We study the Gaussian approximation to the quantum fluctuations of the metric of the four dimensional anti-De Sitter spacetime. The associated massless scalar field has a quartic self interaction, for which we construct the generating functional of the $n$-point correlation functions. The concomitant infrared divergence is cured by a mass renormalization provided by the cosmological constant, which is also responsible for the renormalization of the coupling constant of the field theory.