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 ${\mathrm{H}}^4$ 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.

• Received 31 March 2004

DOI:https://doi.org/10.1103/PhysRevD.69.125015