(0,2) Duality

TL;DR

This paper develops dual descriptions of (0,2) gauged linear sigma models, establishing an analogue of mirror symmetry and computing instanton-corrected chiral rings, advancing understanding of (0,2) supersymmetric theories.

Contribution

It introduces dual formulations of (0,2) models, including Landau-Ginzburg and non-linear sigma models, and computes their instanton-corrected chiral rings, extending mirror symmetry concepts.

Findings

Dual descriptions include Landau-Ginzburg and sigma models.

Computed instanton-corrected chiral rings for examples.

Established a (0,2) analogue of quantum cohomology.

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.