Stable Singularities in String Theory

Abstract

We study a topological obstruction of a very stringy nature concerned with deforming the target space of an $N=2$ non-linear \sm. This target space has a singularity which may be smoothed away according to the conventional rules of geometry but when one studies the associated conformal field theory one sees that such a deformation is not possible without a discontinuous change in some of the correlation functions. This obstruction appears to come from torsion in the homology of the target space (which is seen by deforming the theory by an irrelevant operator). We discuss the link between this phenomenon and orbifolds with discrete torsion as studied by Vafa and Witten.

25 pages and 3 figures, LaTeX with epsf. Appendix by Mark Gross

References in corpus (7)

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• Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3
• Worldsheet Instantons and Torsion Curves, Part A: Direct Computation
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• Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds
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• D-branes on Fourfolds with Discrete Torsion
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• Noncommutative resolutions and CICY quotients from a non-abelian GLSM