Casimir Effect on the brane

TL;DR

This paper investigates how higher-dimensional fields and their localization properties affect the Casimir effect between parallel plates on a brane, revealing conditions under which corrections are exponentially or power-law suppressed.

Contribution

A new method is introduced to compute Casimir energy corrections on a brane, accounting for localization effects and the presence of massless modes.

Findings

Corrections are exponentially suppressed when no massless mode is present.

Presence of a massless mode can lead to sizeable Casimir energy corrections.

Next-to-leading order corrections follow a power-law suppression due to wave function overlap.

Abstract

We consider the Casimir effect between two parallel plates localized on a brane. In order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the KK modes. When no massless mode appears in the spectrum, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. Here we illustrate a new method to compute the correction to the Casimir energy between two parallel plates, localized on a brane. The Casimir energy is suppressed by two factors: at lowest order in $\varepsilon$, the correction comes entirely from the massive mode and turns out to be exponentially suppressed; the next-to-leading order correction in $\varepsilon$ follows, instead, a power-law suppression due to the small wave function overlap of the zero-mode with matter confined on the visible brane. Generic comments on the constraints on new physics that may arise from Casimir force experiments are also made.