Casimir effect in rugby-ball type flux compactifications

TL;DR

This paper analyzes the Casimir effect in a 6D flux compactification model to understand quantum stabilization of the volume modulus and its implications for energy scale hierarchies.

Contribution

It provides a revised calculation of the effective potential using zeta function regularization and explores the physical implications for hierarchy stabilization.

Findings

Larger warping leads to a bigger hierarchy.

Results are consistent with previous work in the non-warped limit.

Quantum corrections influence the stability of extra dimensions.

Abstract

As a continuation of the work in \cite{mns}, we discuss the Casimir effect for a massless bulk scalar field in a 4D toy model of a 6D warped flux compactification model,to stabilize the volume modulus. The one-loop effective potential for the volume modulus has a form similar to the Coleman-Weinberg potential. The stability of the volume modulus against quantum corrections is related to an appropriate heat kernel coefficient. However, to make any physical predictions after volume stabilization, knowledge of the derivative of the zeta function, $\zeta'(0)$ (in a conformally related spacetime) is also required. By adding up the exact mass spectrum using zeta function regularization, we present a revised analysis of the effective potential. Finally, we discuss some physical implications, especially concerning the degree of the hierarchy between the fundamental energy scales on the branes. For a larger degree of warping our new results are very similar to the previous ones \cite{mns} and imply a larger hierarchy. In the non-warped (rugby-ball) limit the ratio tends to converge to the same value, independently of the bulk dilaton coupling.