A (0,2) mirror duality

TL;DR

This paper constructs exactly solvable (0,2) heterotic string compactifications, revealing a mirror duality via a quotient procedure, and interprets this duality geometrically within hybrid models, extending known (2,2) mirror symmetry concepts.

Contribution

It introduces a new class of exactly solvable (0,2) models with a mirror duality, generalizing Gepner models and providing a geometric interpretation in hybrid models.

Findings

Constructed (0,2) heterotic compactifications with mirror duality.

Identified moduli spaces with geometric limits involving Calabi-Yau spaces.

Realized mirror symmetry through a quotient procedure at exactly solved points.

Abstract

We construct a class of exactly solved (0,2) heterotic compactifications, similar to the (2,2) models constructed by Gepner. We identify these as special points in moduli spaces containing geometric limits described by non-linear sigma models on complete intersection Calabi-Yau spaces in toric varieties, equipped with a bundle whose rank is strictly greater than that of the tangent bundle. These moduli spaces do not in general contain a locus exhibiting (2,2) supersymmetry. A quotient procedure at the exactly solved point realizes the mirror isomorphism, as was the case for Gepner models. We find a geometric interpretation of the mirror duality in the context of hybrid models.