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Resolving singularities in \((0,2)\) models. (English) Zbl 1049.81585
Summary: 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 \(K3\).

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J81 Relationships between surfaces, higher-dimensional varieties, and physics
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