Quantum Stabilization of Compact Space by Extra Fuzzy Space

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.