Topological heterotic rings

Abstract

We prove the existence of topological rings in $(0,2)$ theories containing non-anomalous left-moving $U(1)$ currents by which they may be twisted. While the twisted models are not topological, their ground operators form a ring under non-singular OPE which reduces to the $(a,c)$ or $(c,c)$ ring at $(2,2)$ points and to a classical sheaf cohomology ring at large radius, defining a quantum sheaf cohomology away from these special loci. In the special case of Calabi–Yau compactifications, these rings are shown to exist globally on the moduli space if the rank of the holomorphic bundle is less than eight.