Resolving singularities in \((0,2)\) models.

*(English)*Zbl 1049.81585Summary: 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 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 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 non-perturbative treatment for their resolution and briefly discuss applications to heterotic models on \(K3\).