Recent Developments in (0,2) Mirror Symmetry

TL;DR

This paper reviews recent progress in (0,2) mirror symmetry, a generalization of mirror symmetry to heterotic strings, highlighting new examples, theoretical ideas, and open questions in this emerging field.

Contribution

It summarizes recent developments in (0,2) mirror symmetry, including quantum sheaf cohomology, mirror maps, and new examples like Hirzebruch surfaces.

Findings

Introduction of (0,2) mirror pairs from worldsheet duality

Development of quantum sheaf cohomology theory

Construction of (0,2) mirrors for Hirzebruch surfaces

Abstract

Mirror symmetry of the type II string has a beautiful generalization to the heterotic string. This generalization, known as (0,2) mirror symmetry, is a field still largely in its infancy. We describe recent developments including the ideas behind quantum sheaf cohomology, the mirror map for deformations of (2,2) mirrors, the construction of mirror pairs from worldsheet duality, as well as an overview of some of the many open questions. The (0,2) mirrors of Hirzebruch surfaces are presented as a new example.