Noncommutative Supertori in Two Dimensions

Details Noncommutative Supertori in Two Dimensions Noncommutative Supertori in Two Dimensions

2008-07-04

arxiv.org/abs/0807.0710v1

JHEP 0808:058,2008

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX 17 pages

Scientific paper

10.1088/1126-6708/2008/08/058

First we consider the deformations of superspaces with N=(1,1) and N=(2,2) supersymmetries in two dimensions. Among these the construction of noncommutative supertorus with odd spin structure is possible only in the case of N=(2,2) supersymmetry broken down to N=(1,1). However, for the even spin structures the construction of noncommutative supertorus is possible for both N=(1,1) and N=(2,2) cases. The spin structures are realized by implementing the translational properties along the cycles of commutative supertorus in the operator version: Odd spin structure is realized by the translation in the fermionic direction in the same manner as in the construction of noncommutative torus, and even spin structures are realized with appropriate versions of the spin angular momentum operator.

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