Gauged (2,2) Sigma Models and Generalized Kahler Geometry

TL;DR

This paper explores gauged (2,2) supersymmetric sigma models with bihermitian target space geometry, analyzing moment maps, T-duality, and their relation to generalized complex structures, with explicit examples like the SU(2) x U(1) WZNW model.

Contribution

It introduces a formulation of gauged (2,2) sigma models using semi-chiral superfields and connects bihermitian geometry with generalized complex structures and T-duality.

Findings

Moment map construction in gauged sigma models.

Explicit T-duality example involving semi-chiral superfields.

Connection between bihermitian geometry and generalized complex structures.

Abstract

We gauge the (2,2) supersymmetric non-linear sigma model whose target space has bihermitian structure (g, B, J_{\pm}) 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) x 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.