Thermal states in Anti-de Sitter space-time and the role of time-like   infinity
  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. 
L. Vanzo and G. Turco