Bulk quantum effects for de Sitter branes in AdS(5)

TL;DR

This paper analyzes quantum corrections for de Sitter branes in AdS(5), focusing on one-loop effective actions, boundary conditions, and the induced higher curvature terms, highlighting the importance of cocycle functions and zero mode subtleties.

Contribution

It provides a detailed calculation of quantum corrections for de Sitter branes in AdS(5), including the effective action for spinor fields and the role of cocycle functions, which was not previously fully understood.

Findings

Quantum corrections induce higher order curvature terms.

Cocycle functions cannot generally be removed by renormalisation.

Zero mode subtleties significantly affect physical results.

Abstract

We investigate some issues regarding quantum corrections for de Sitter branes in a bulk 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 renormalisation. 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 non-zero and must be included. Subtleties with any zero modes are also discussed.