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

TL;DR

This paper establishes conditions for constructing N=(2,2) supersymmetric gauged sigma models with three-form flux using twisted generalized Kaehler geometry, extending traditional quotient methods.

Contribution

It introduces a geometric framework linking twisted generalized Kaehler structures and supersymmetric gauged sigma models with flux, broadening the scope of model construction.

Findings

Conditions for supersymmetry involve twisted generalized Kaehler structures.

The quotient of such structures remains twisted generalized Kaehler.

New models with NS flux can be generated beyond traditional methods.

Abstract

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 Kaehler 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 Kaehler 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 Kaehler quotient construction based on Kaehler gauged sigma models.