Finite-Temperature Casimir Effect on the Radius Stabilization of Noncommutative Torus

TL;DR

This paper investigates how finite-temperature quantum effects influence the stability of extra noncommutative dimensions in a higher-dimensional spacetime, revealing conditions under which these dimensions can be stabilized by Casimir energy.

Contribution

It provides a novel analysis of the finite-temperature Casimir effect on noncommutative tori, showing potential stabilization mechanisms for extra dimensions in high-temperature regimes.

Findings

Casimir energy is independent of radius for L=1.

For L>1, Casimir energy can be repulsive and stabilize the extra dimensions.

Stabilization occurs when d-L is a non-negative even integer.

Abstract

The one-loop correction to the spectrum of Kaluza-Klein system for the $\phi^3$ model on $R^{1,d}\times (T_\theta^2)^L$ is evaluated in the high temperature limit, where the $1+d$ dimensions are the ordinary flat Minkowski spacetimes and the $L$ extra two-dimensional tori are chosen to be the noncommutative torus with noncommutativity $\theta$. The corrections to the Kaluza-Klein mass formula are evaluated and used to compute the Casimir energy with the help of the Schwinger perturbative formula in the zeta-function regularization method. The results show that the one-loop Casimir energy is independent of the radius of torus if L=1. However, when $L>1$ the Casimir energy could give repulsive force to stabilize the extra noncommutative torus if $d-L$ is a non-negative even integral. This therefore suggests a possible stabilization mechanism of extra radius in high temperature, when the extra spaces are noncommutative.