Casimir Effect on the Radius Stabilization of the Noncommutative Torus

TL;DR

This paper investigates how quantum corrections and noncommutative geometry influence the stability of extra dimensions in a higher-dimensional field theory, revealing conditions under which Casimir energy can stabilize noncommutative tori.

Contribution

It provides a detailed calculation of the one-loop correction to Kaluza-Klein spectra and the resulting Casimir energy in a noncommutative torus setting, highlighting stabilization mechanisms.

Findings

Casimir energy can be repulsive for L>2 in certain dimensions.

Noncommutativity affects the spectrum and stabilization of extra dimensions.

Stability conditions depend on the number of noncommutative tori and spacetime dimensions.

Abstract

We evaluate the one-loop correction to the spectrum of Kaluza-Klein system for the $\phi^3$ model on $R^{1,d}\times (T_\theta^2)^L$, where $1+d$ dimensions are the ordinary flat Minkowski spacetimes and the extra dimensions are the L two-dimensional noncommutative tori with noncommutativity $\theta$. The correction to the Kaluza-Klein mass spectrum is then used to compute the Casimir energy. The results show that when $L>2$ the Casimir energy due to the noncommutativity could give repulsive force to stabilize the extra noncommutative tori in the cases of $d = 4n - 2$, with $n$ a positive integral.