Resolving Singularities in (0,2) Models

TL;DR

This paper investigates singularities in (0,2) string models, proposing perturbative resolutions and exploring the emergence of gauge sheaves, with implications for N=1 string compactifications.

Contribution

It introduces a method for resolving certain (0,2) singularities perturbatively and highlights the role of gauge sheaves in supersymmetric sigma-models.

Findings

Perturbative resolution of some (0,2) singularities

Emergence of gauge sheaves as structures for fermion coupling

Identification of singularities requiring nonperturbative treatment

Abstract

In contrast to the familiar (2,2) case, the singularities which arise in the (0,2) setting can be associated with degeneration of the base Calabi-Yau manifold {\it and/or}\/ with degenerations of the gauge bundle. We study a variety of such singularities and give a procedure for resolving those which can be cured perturbatively. Among the novel features which emerge are models in which smoothing singularities in the base yields a gauge {\it sheaf}\/ as opposed to a gauge bundle as the structure to which left moving fermions couple. Supersymmetric $\sigma$-models with target data being an appropriate sheaf on a Calabi-Yau space therefore appear to be the natural arena for N=1 string models in four dimensions. We also indicate a variety of singularities which would require a nonperturbative treatment for their resolution and briefly discuss applications to heterotic models on K3.