(0,2) Duality

TL;DR

The work develops a non-perturbative duality for (0,2) GLSMs, generating exact dual descriptions that can be either (0,2) Landau-Ginzburg theories or nonlinear sigma models, depending on the left-moving bundle rank relative to the tangent bundle. By extending Hori–Vafa-style abelian duality to (0,2) theories and incorporating vortex instantons, the authors derive an exact dual superpotential and a generalized chiral ring that reduces to quantum cohomology in special (2,2) cases. They analyze vacuum structures, R-symmetry constraints, and instanton corrections, showing how dual descriptions map Kähler moduli to superpotential terms and how bundle deformations induce chiral-ring mixing. The paper provides numerous explicit dual pairs, including conformal models and various bundle deformations, offering a framework for exploring heterotic string compactifications and (0,2) mirror-like phenomena with potential applications to quantum cohomology generalizations and heterotic instanton corrections.

Abstract

We construct dual descriptions of (0,2) gauged linear sigma models. In some cases, the dual is a (0,2) Landau-Ginzburg theory, while in other cases, it is a non-linear sigma model. The duality map defines an analogue of mirror symmetry for (0,2) theories. Using the dual description, we determine the instanton corrected chiral ring for some illustrative examples. This ring defines a (0,2) generalization of the quantum cohomology ring of (2,2) theories.