Quantum Stabilization of Compact Space by Extra Fuzzy Space

TL;DR

This paper explores how quantum effects of scalar fields on a specific higher-dimensional spacetime with fuzzy extra dimensions can lead to a repulsive Casimir force, potentially stabilizing the size of extra dimensions.

Contribution

It introduces a model with fuzzy extra space and calculates quantum corrections, revealing conditions under which the Casimir energy stabilizes the compact dimensions.

Findings

Casimir energy can be repulsive for certain dimensions

Quantum corrections stabilize the size of extra dimensions

Fuzzy space influences vacuum energy behavior

Abstract

We investigate the quantized scalar field on the Kaluza-Klein spacetimes of $M^D\times T^d \times S_{FZ}$, where $M^D$ is the ordinary $D$ dimensional flat Minkowski spacetimes, $T^d $ is the $d$ dimensional commutative torus, and $S_{FZ}$ is a noncommutative fuzzy two sphere with a fixed quantized radius. After evaluating the one-loop correction to the spectrum we use the mass-corrected term to compute the Casimir energy of the scalar field on the model spacetime. It is seen that, for some values of $D$ and $d$, the Casimir energy due to vacuum fluctuation in the model spacetimes could give rise a repulsive force to stabilize the commutative torus.