Fermionic T-duality and Morita Equivalence

Details Fermionic T-duality and Morita Equivalence Fermionic T-duality and Morita Equivalence

2011-01-03

arxiv.org/abs/1101.0473v4

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, the version appeared in JHEP

Scientific paper

In this paper we investigate the relationship between the so-called fermionic T-duality and the Morita equivalence of noncommutative supertori. We first get an action satisfying the BRST invariance under nonvanishing constant R-R and NS-NS backgrounds in the hybrid formalism. We investigate the effect of bosonic T-duality transformation together with fermionic T-duality transformation in this background and look for the resultant symmetry of transformations. We find that the duality transformations correspond to Morita equivalence of noncommutative supertori. In particular, we obtain the symmetry group $SO(2,2,{\cal V}_{\Z}^0)$ in two dimensions, where ${\cal V}_{\Z}^0$ denotes Grassmann even number whose body part belongs to ${\Z}$.

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