Recent Developments in (0,2) Mirror Symmetry

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.

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Cited by in corpus (27)

• Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications
• A Metric for Heterotic Moduli
• Notes on nonabelian (0,2) theories and dualities
• A proposal for nonabelian (0,2) mirrors
• N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
• Quantum sheaf cohomology on Grassmannians
• General aspects of heterotic string compactifications on stacks and gerbes
• On the Effective Field Theory of Heterotic Vacua
• A proposal for (0,2) mirrors of toric varieties
• Classical sheaf cohomology rings on Grassmannians
• Analogues of Mathai-Quillen forms in sheaf cohomology and applications to topological field theory
• On Isometry Anomalies in Minimal N=(0,1) and N=(0,2) Sigma Models
• More Toda-like (0,2) mirrors
• Small gauge transformations and universal geometry in heterotic theories
• A proposal for nonabelian mirrors
• A few recent developments in 2d (2,2) and (0,2) theories
• (2,2) Geometry from Gauge Theory
• Nonabelian mirrors and Gromov-Witten invariants
• Testing the (0,2) mirror map
• Anomalies of Minimal N=(0, 1) and N=(0, 2) Sigma Models on Homogeneous Spaces
• Moduli in General $SU(3)$-Structure Heterotic Compactifications
• On Grassmannian Heterotic Sigma Model
• More on Two-Dimensional $O(N)$ Models with $\mathcal{N}=(0,1)$ Supersymmetry
• A (0,2) mirror duality
• Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications
• Heterotic Flux Geometry from Chiral Gauge Dynamics
• Global aspects of (0,2) moduli space: toric varieties and tangent bundles