The Effective Action in Gauged Supergravity on Hyperbolic Background and   Induced Cosmological Constant
  The one-loop effective action for 4-dimensional gauged supergravity with negative cosmological constant, is investigated in space-times with compact hyperbolic spatial section. The explicit expansion of the effective action as a power series of the curvature on hyperbolic background is derived, making use of heat-kernel and zeta-regularization techniques. The induced cosmological and Newton constants are computed. 
A.A. Bytsenko, S.D. Odintsov and s. Zerbini