Thermal states in Anti-de Sitter space-time and the role of time-like infinity

TL;DR

This paper explores the thermodynamic properties of quantum fields in anti-de Sitter space-time, emphasizing how the boundary at time-like infinity influences free energy at finite temperature and charge.

Contribution

It introduces a Mellin complex representation for the thermodynamic potential and analyzes the impact of time-like infinity as a boundary on thermal states.

Findings

Time-like infinity acts as a boundary affecting free energy.

High temperature behavior of thermal states is characterized.

Mellin complex representation aids in thermodynamic analysis.

Abstract

The grand-canonical thermodynamic potential for Bose and Fermi fields in anti-de Sitter space-time is introduced and a Mellin complex representation is given. This is used to investigate the high temperature properties of the thermal state at finite charge. The time-like nature of spatial infinity is shown to act as a boundary, and changes the free energy of the field in thermal equilibrium.