T-duality, quotients and generalized Kahler geometry

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.

18 pages

References in corpus (15)

• Duality, Quotients, and Currents
• Generalized complex manifolds and supersymmetry
• Symmetries in generalized Kähler geometry
• Topological sigma-models with H-flux and twisted generalized complex manifolds
• Generalized complex geometry, generalized branes and the Hitchin sigma model
• Off-Shell Formulation of N=2 Non-Linear Sigma-Models
• Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models
• NS-NS fluxes in Hitchin's generalized geometry
• Generalized Kahler Geometry from supersymmetric sigma models
• Some Aspects of N=(2,2), D=2 Supersymmetry
• The biHermitian topological sigma model
• A potential for Generalized Kahler Geometry
• D=2 N=(2,2) Semi Chiral Vector Multiplet
• Reduction of twisted generalized Kähler structure
• The Geometry of Supersymmetric Sigma-Models

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• The Large Vector Multiplet Action
• The Semi-Chiral Quotient, Hyperkahler Manifolds and T-duality
• The world-sheet description of A and B branes revisited
• Off-shell N=(4,4) supersymmetry for new (2,2) vector multiplets
• T-Duality in $(2,1)$ Superspace
• On gauged linear sigma models with torsion
• The complex world of superstrings: On semichiral sigma models