Casimir force for a scalar field in warped brane worlds

TL;DR

This paper calculates the 4D Casimir force for a scalar field in a warped brane world scenario, revealing how extra dimensions influence low-energy quantum forces through mode contributions.

Contribution

It provides a detailed method to compute the Casimir force in a Randall-Sundrum model with an extra dimension, highlighting the impact of mode structure on observable forces.

Findings

Standard 4D Casimir force recovered at low energy

Extra dimensions add an additional term to the force

Mode contributions depend on their wave functions on the brane

Abstract

In looking for imprints of extra dimensions in brane world models one usually builts these so that they are compatible with known low energy physics and thus focuses on high energy effects. Nevertheless, just as submillimeter Newton's law tests probe the mode structure of gravity other low energy tests might apply to matter. As a model example, in this work we determine the 4D Casimir force corresponding to a scalar field subject to Dirichlet boundary conditions on two parallel planes lying within the single brane of a Randall-Sundrum scenario extended by one compact extra dimension. Using the Green's function method such a force picks the contribution of each field mode as if it acted individually but with a weight given by the square of the mode wave functions on the brane. In the low energy regime one regains the standard 4D Casimir force that is associated to a zero mode in the massless case or to a quasilocalized or resonant mode in the massive one whilst the effect of the extra dimensions gets encoded as an additional term.