The general (2, 2) gauged sigma model with three-form flux

We find the conditions under which a Riemannian manifold equipped with a closed three-form and a vector field define an on-shell N = (2, 2) supersymmetric gauged sigma model. The conditions are that the manifold admits a twisted generalized Kähler structure, that the vector field preserves this structure, and that a so-called generalized moment map exists for it. By a theorem in generalized complex geometry, these conditions imply that the quotient is again a twisted generalized Kähler manifold; this is in perfect agreement with expectations from the renormalization group flow. This method can produce new N = (2, 2) models with NS flux, extending the usual Kähler quotient construction based on Kähler gauged sigma models.