Gauged (2,2) sigma models and generalized Kähler geometry

Abstract

We gauge the (2, 2) supersymmetric non-linear sigma model whose target space has bihermitian structure (g, B, J±) with noncommuting complex structures. The bihermitian geometry is realized by a sigma model which is written in terms of (2, 2) semi-chiral superfields. We discuss the moment map, from the perspective of the gauged sigma model action and from the integrability condition for a Hamiltonian vector field. We show that for a concrete example, the SU(2) × U(1) WZNW model, as well as for the sigma models with almost product structure, the moment map can be used together with the corresponding Killing vector to form an element of T⊕T* which lies in the eigenbundle of the generalized almost complex structure. Lastly, we discuss T-duality at the level of a (2,2) sigma model involving semi-chiral superfields and present an explicit example.