T-duality, quotients and generalized Kähler geometry

We reopen the discussion of gauging two-dimensional off-shell (2,2) supersymmetric sigma models written in terms of semichiral superfields. The gauging 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. These Killing potentials lead to generalized moment maps. Next we construct the T-duality map, while keeping (2,2) supersymmetry manifest. In the T-dual description, a pair of left and right semichiral superfields is replaced by a pair of chiral and twisted chiral multiplets. We end with a discussion on quotient construction.