On partition functions and phases of scalars in AdS

Abstract

We study the phases of scalar field theories in thermal AdSd+1 spaces for d = 1, 2, 3. The analysis is done for theories with global O(N) symmetry for 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 AdSd+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.