On partition functions and phases of scalars in AdS

TL;DR

This paper analyzes the phase structure of scalar fields in thermal AdS spaces with various dimensions, identifying symmetry phases and introducing a method for computing one-loop partition functions applicable to arbitrary dimensions.

Contribution

It provides a comprehensive analysis of scalar field phases in thermal AdS spaces and introduces a general method for calculating one-loop partition functions using eigenfunctions of the Laplacian.

Findings

Identified symmetry-preserving and symmetry-breaking phases as functions of mass and temperature.

Developed a method for computing one-loop partition functions on thermal AdS for arbitrary dimensions.

Reproduced known results in the literature using the new method.

Abstract

We study the phases of scalar field theories in thermal $AdS_{d+1}$ spaces for $d=1,2,3$. The analysis is done for theories with global $O(N)$ symmetry for the finite as well as large $N$. The symmetry-preserving and symmetry-breaking phases are identified as a function of the mass-squared of the scalar field and temperature. On the way we also describe a method for computing one-loop partition function for scalar field on thermal $AdS_{d+1}$ for arbitrary $d$ that reproduces results known in the literature. The derivation is based on the method of images and uses the eigenfunctions of the Laplacian on Euclidean $AdS$.