Conjectures on (0,2) Mirror Symmetry

TL;DR

This paper proposes a new conjecture for (0,2) mirror symmetry, extending the monomial-divisor mirror map to include tangent bundle deformations, and verifies it in simple cases.

Contribution

It introduces a conjectural reformulation of the mirror map applicable at moduli space boundaries, advancing understanding of (0,2) mirror symmetry.

Findings

Conjecture verified in simple cases

Extension of mirror map to tangent bundle deformations

Provides a calculational framework using sheaf descriptions

Abstract

In this paper we conjecture a reformulation of the monomial-divisor mirror map for (2,2) mirror symmetry, valid at a boundary of the moduli space, that is easily extended to also include tangent bundle deformations -- an important step towards understanding (0,2) mirror symmetry. We check our conjecture in a few simple cases, and thereby illustrate how to perform calculations using a description of sheaves recently published by Knutson, Sharpe.