  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.
