T-duality, quotients and generalized Kahler geometry

TL;DR

This paper explores the gauging of (2,2) supersymmetric sigma models with generalized Kahler target spaces, introduces a new vector multiplet, and discusses T-duality and quotient constructions within this framework.

Contribution

It introduces a new semichiral vector multiplet for gauging, clarifies the role of Killing potentials, and demonstrates T-duality preserving supersymmetry in generalized Kahler geometry.

Findings

Identified three Killing potentials for gauged sigma models.

Established the connection between Killing potentials and twisted generalized Kahler geometry.

Constructed a T-duality map swapping semichiral with chiral/twisted chiral superfields.

Abstract

In this paper we reopen the discussion of gauging the two-dimensional off-shell (2,2) supersymmetric sigma models written in terms of semichiral superfields. The associated target space geometry of this particular sigma model is generalized Kahler (or bi-hermitean with two non-commuting complex structures). The gauging of the isometries of the sigma model is now done by coupling the semichiral superfields to the new (2,2) semichiral vector multiplet. We show that the two moment maps together with a third function form the complete set of three Killing potentials which are associated with this gauging. We show that the Killing potentials lead to the generalized moment maps defined in the context of twisted generalized Kahler geometry. Next we address the question of the T-duality map, while keeping the (2,2) supersymmetry manifest. Using the new vector superfield in constructing the duality functional, under T-duality we swap a pair of left and right semichiral superfields by a pair of chiral and twisted chiral multiplets. We end with a discussion on quotient construction.