Casimir effect between anti-de Sitter braneworlds

TL;DR

This paper computes the quantum Casimir effect for a scalar field in an anti-de Sitter braneworld, revealing significant corrections to the radion potential at small brane separations.

Contribution

It introduces a method to calculate the one-loop effective action in a detuned Randall-Sundrum scenario with anti-de Sitter branes, using conformal transformations and cocycle functions.

Findings

Casimir potential significantly affects radion stabilization.

Quantum corrections are sizable for small brane separations.

Method can be applied to other curved brane configurations.

Abstract

We calculate the one-loop effective action of a scalar field with general mass and coupling to the curvature in the detuned Randall-Sundrum brane world scenario, where the four-dimensional branes are anti-de Sitter. We make use of conformal transformations to map the problem to one on the direct product of the hyperbolic space H^4 and the interval. We also include the cocycle function for this transformation. This Casimir potential is shown to give a sizable correction to the classical radion potential for small values of brane separation.