Partition functions for $U(1)$ vectors and phases of scalar QED in AdS

Abstract

We extend the computation of one-loop partition function in AdS${}_{d+1}$ using the method in [arXiv:2201.09043] and [arXiv:2303.02711] for scalars and fermions to the case of $U(1)$ vectors. This method utilizes the eigenfunctions of the AdS Laplacian for vectors. For finite temperature, the partition function is obtained by generalizing the eigenfunctions so that they are invariant under the quotient group action, which defines the thermal AdS spaces. The results obtained match with those available in the literature. As an application of these results, we then analyze phases of scalar QED theories at one-loop in $d=2,3$. We do this first as functions of AdS radius at zero temperature showing that the results reduce to those in flat space in the large AdS radius limit. Thereafter the phases are studied as a function of the scalar mass and temperature. We also derive effective potentials and study phases of the scalar QED theories with $N$ scalars.

33+10 pages, v3: published version

References in corpus (7)

• Consistent Use of Effective Potentials
• Conformal field theories in anti-de Sitter space
• Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
• Fermions in AdS and Gross-Neveu BCFT
• Loops in AdS: From the Spectral Representation to Position Space II
• On partition functions and phases of scalars in AdS
• Phases of theories with fermions in AdS