We investigate some issues regarding quantum corrections for de Sitter branes in a bulk ${\mathrm{AdS}}_5$ spacetime. The one-loop effective action for a Majorana spinor field is evaluated and compared with the scalar field result. We also evaluate the cocycle function for various boundary conditions, finding that the quantum corrections naturally induce higher order curvature terms in the original action and, in general, it is not possible to eliminate the cocycle function by renormalization. In the one brane limit care must be taken on how one extracts physical results. The effective potential is found to be zero on the conformally related cylinder. However, using the actual metric, the contribution from the cocycle function is nonzero and must be included. Subtleties with any zero modes are also discussed.

• Received 24 March 2003

DOI:https://doi.org/10.1103/PhysRevD.67.125010