Radion effective potential in the Brane-World

TL;DR

This paper investigates how Casimir forces from bulk fields in warped extra dimensions can stabilize the radion in brane-world models, with implications for hierarchy problem solutions and radion mass scales.

Contribution

It calculates the one-loop effective potential for the radion induced by bulk fields in Randall-Sundrum models, highlighting the conditions for stabilization and radion mass implications.

Findings

Casimir force can stabilize the radion in warped geometries.

The radion mass from Casimir effects is hierarchically smaller than TeV scale.

Additional mechanisms are needed for radion mass to meet observational constraints.

Abstract

We show that in brane-world scenarios with warped extra dimensions, the Casimir force due to bulk matter fields may be sufficient to stabilize the radion field $\phi$. In particular, we calculate one loop effective potential for $\phi$ induced by bulk gravitons and other possible massless bulk fields in the Randall-Sundrum background. This potential has a local extremum, which can be a maximum or a minimum depending on the detailed bulk matter content. If the parameters of the background are chosen so that the hierarchy problem is solved geometrically, then the radion mass induced by Casimir corrections is hierarchycally smaller than the $TeV$. Hence, in this important case, we must invoke an alternative mechanism (classical or nonperturbative) which gives the radion a sizable mass, to make it compatible with observations.