T-duality and Generalized Complex Geometry

TL;DR

This paper explicitly derives T-duality transformations in the phase space of the N=(1,1) sigma model, demonstrating its symplectic nature, its relation to O(d,d), and its preservation of extended supersymmetry.

Contribution

It provides explicit formulas for T-duality transformations in phase space and shows their properties in relation to generalized complex structures and supersymmetry.

Findings

T-duality acts as a symplectomorphism in phase space.

T-duality transformations are elements of O(d,d).

Extended supersymmetry is preserved under T-duality.

Abstract

We find the explicit T-duality transformation in the phase space formulation of the N=(1,1) sigma model. We also show that the T-duality transformation is a symplectomorphism and it is an element of O(d,d). Further, we find the explicit T-duality transformation of a generalized complex structure in this model. We also show that the extended supersymmetry of the sigma model is preserved under the T-duality.