  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.
