Quantized bulk scalar fields in the Randall-Sundrum brane model

We examine the lowest order quantum corrections to the effective action ari sing from a quantized real scalar field in the Randall-Sundrum background s pacetime. The leading term is the familiar vacuum, or Casimir, energy densi ty. The next term represents an induced gravity term that can renormalize t he 4-dimensional Newtonian gravitational constant. The calculations are per formed for an arbitrary spacetime dimension. Two inequivalent boundary cond itions, corresponding to twisted and untwisted field configurations, are co nsidered. A careful discussion of the regularization and renormalization of the effective action is given, with the relevant counterterms found. It is shown that the requirement of self-consistency of the Randall-Sundrum solu tion is not simply a matter of minimizing the Casimir energy density. The m assless, conformally coupled scalar field results are obtained as a special limiting case of our results. We clarify a number of differences with prev ious work. (C) 2001 Published by Elsevier Science B.V.