L. Vanzo et G. Turco, THERMAL STATES IN ANTI-DE SITTER SPACE-TIME AND THE ROLE OF TIME-LIKEINFINITY, Physical review. D. Particles and fields, 50(8), 1994, pp. 5148-5154
The grand-canonical thermodynamic potential for Bose and Fermi fields
in anti-de Sitter space-time is introduced and a Mellin complex repres
entation is given. This is used to investigate the high temperature pr
operties of the thermal state at finite charge. The timelike nature of
spatial infinity is shown to act as a boundary, and changes the free
energy of the field in thermal equilibrium.