Massive-scalar effective actions on anti-de Sitter space-time

Abstract

Closed forms are derived for the effective actions for free, massive spinless fields in anti-de Sitter space-times in arbitrary dimensions. The results have simple expressions in terms of elementary functions (for odd dimensions) or multiple Gamma functions (for even dimensions). We use these to argue against the quantum validity of Cruz' recently proposed duality relating such theories with differing masses and cosmological constants.PACS Nos. 11.10- z, 11.90+ t, and 04.60-m.