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Equivalences Between GIT Quotients of Landau-Ginzburg B-Models

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Abstract

We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of Landau-Ginzburg B-models that arise as different GIT quotients of a vector space by a one-dimensional torus, and show that for each such pair the two categories of B-branes are quasi-equivalent. In fact we produce a whole set of quasi-equivalences indexed by the integers, and show that the resulting auto-equivalences are all spherical twists.

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  1. Department of Mathematics, Imperial College of London, London, SW7 2BW, United Kingdom

    Ed Segal

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  1. Ed Segal
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Correspondence to Ed Segal.

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Communicated by A. Kapustin

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Segal, E. Equivalences Between GIT Quotients of Landau-Ginzburg B-Models. Commun. Math. Phys. 304, 411–432 (2011). https://doi.org/10.1007/s00220-011-1232-y

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  • DOI: https://doi.org/10.1007/s00220-011-1232-y

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