On partition functions and phases of scalars in AdS

Abstract

We study the phases of scalar field theories in thermal $Ad{S}_{d+1}$ 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 $Ad{S}_{d+1}$ 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 $AdS$.

33+9 pages,v2: published version

References in corpus (3)

• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Thermal Order in Conformal Theories
• Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions

Cited by in corpus (3)

• Phases of theories with fermions in AdS
• Constraining dimension-6 SMEFT with higher-order predictions for $pp\to tW$
• Partition functions for $U(1)$ vectors and phases of scalar QED in AdS