Fermionic T-duality and Morita Equivalence

TL;DR

This paper explores the connection between fermionic T-duality and Morita equivalence in noncommutative supertori, revealing a symmetry group that characterizes their relationship in string theory backgrounds.

Contribution

It demonstrates that fermionic and bosonic T-duality transformations correspond to Morita equivalence of noncommutative supertori, establishing a new symmetry group in this context.

Findings

Duality transformations correspond to Morita equivalence.

Identified symmetry group $SO(2,2,{ m V}_{ m Z}^0)$ in two dimensions.

Action satisfying BRST invariance in specific backgrounds.

Abstract

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 ${\Z}$.