GLSMs for non-Kahler Geometries

We identify a simple mechanism by which H-flux satisfying the modified Bianchi identity arises in garden-variety (0,2) gauged linear sigma models. Taking suitable limits leads to effective gauged linear sigma models with Green-Schwarz anomaly cancellation. We test the quantum-consistency of a class of such effective theories by constructing an off-shell superconformal algebra, providing evidence that these models run to good CFTs in the deep IR.