Topological Heterotic Rings

TL;DR

This paper demonstrates the existence of topological rings in (0,2) theories with non-anomalous U(1) currents, connecting quantum sheaf cohomology with classical sheaf cohomology across moduli space.

Contribution

It establishes the existence of topological rings in (0,2) theories and describes their structure and behavior in Calabi-Yau compactifications.

Findings

Ground operators form a ring under non-singular OPE

Ring reduces to (a,c) or (c,c) ring at (2,2) points

Quantum sheaf cohomology defined away from special loci

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.