Casimir Force in Compact Noncommutative Extra Dimensions and Radius Stabilization

TL;DR

This paper calculates the Casimir energy in a space with noncommutative extra dimensions, revealing conditions under which the extra dimensions can be stabilized or destabilized due to quantum effects.

Contribution

It introduces a novel analysis of Casimir energy in noncommutative compact spaces, showing how noncommutativity influences force directions and potential stabilization.

Findings

Noncommutative scalar fields produce an attractive Casimir force leading to instability.

Vector fields with periodic boundary conditions can generate a repulsive force for dimensions greater than five.

Potential stabilization of extra dimensions in Kaluza-Klein scenarios with noncommutative geometry.

Abstract

We compute the one loop Casimir energy of an interacting scalar field in a compact noncommutative space of $R^{1,d}\times T^2_\theta$, where we have ordinary flat $1+d$ dimensional Minkowski space and two dimensional noncommuative torus. We find that next order correction due to the noncommutativity still contributes an attractive force and thus will have a quantum instability. However, the case of vector field in a periodic boundary condition gives repulsive force for $d>5$ and we expect a stabilized radius. This suggests a stabilization mechanism for a senario in Kaluza-Klein theory, where some of the extra dimensions are noncommutative.