A proposal for (0,2) mirrors of toric varieties

TL;DR

This paper introduces (0,2) mirror models for Fano toric varieties with specific tangent bundle deformations, matching known (2,2) mirrors and verified through supersymmetric localization techniques.

Contribution

It proposes a new class of (0,2) mirror models for Fano toric varieties, extending mirror symmetry to include certain tangent bundle deformations.

Findings

(0,2) mirrors match Chen et al's results for specific examples.

Closed-string correlators agree between original and mirror models.

Supersymmetric localization provides insights into mirror constructions.

Abstract

In this paper we propose (0,2) mirrors for general Fano toric varieties with special tangent bundle deformations, corresponding to subsets of toric deformations. Our mirrors are of the form of (B/2-twisted) (0,2) Landau-Ginzburg models, matching Hori-Vafa mirrors on the (2,2) locus. We compare our predictions to (0,2) mirrors obtained by Chen et al for certain examples of toric varieties, and find that they match. We also briefly outline conjectures for analogous results for hypersurfaces in Fano toric varieties. Our methods utilize results from supersymmetric localization, which allows us to incidentally gain occasional further insights into GLSM-based (2,2) mirror constructions. For example, we explicitly verify that closed-string correlation functions of the original A-twisted GLSM match those of the mirror B-twisted Landau-Ginzburg model, as well as (0,2) deformations thereof.