Quantum Stabilization of Compact Space by Extra Fuzzy Space

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.

13 pages

References in corpus (7)

• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Scaling Limits of the Fuzzy Sphere at one Loop
• Perturbative dynamics on fuzzy S^2 and RP^2
• Noncommutative Gauge Theories on Fuzzy Sphere and Fuzzy Torus from Matrix Model
• D-brane Solutions in Non-Commutative Gauge Theory on Fuzzy Sphere
• Matrix dynamics of fuzzy spheres

Cited by in corpus (4)

• Thermodynamics on Fuzzy Spacetime
• Boundaries in the Moyal plane
• Effective Potential on Fuzzy Sphere
• Kaluza-Klein Pistons with non-Commutative Extra Dimensions