Quantum stabilization of compact space by extra fuzzy space

We investigate the quantized scalar field on the Kaluza–Klein spacetimes of MD×Td×SFZ, where MD is the ordinary D-dimensional flat Minkowski spacetimes, Td is the d-dimensional commutative torus, and SFZ 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.