Casimir Force in Compact Noncommutative Extra Dimensions and Radius Stabilization


We compute the one loop Casimir energy of an interacting scalar field in a compact noncommutative space of R1,d×Tθ2R^{1,d}\times T^2_\theta, where we have ordinary flat 1+d1+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>5d>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.Comment: 10 pages, TeX, harvma

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