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Vortex Counting and Lagrangian 3-Manifolds

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Abstract

To every 3-manifold M one can associate a two-dimensional \({\mathcal{N}=(2, 2)}\) supersymmetric field theory by compactifying five-dimensional \({\mathcal{N}=2}\) super-Yang–Mills theory on M. This system naturally appears in the study of half-BPS surface operators in four-dimensional \({\mathcal{N}=2}\) gauge theories on one hand, and in the geometric approach to knot homologies, on the other. We study the relation between vortex counting in such two-dimensional \({\mathcal{N}=(2, 2)}\) supersymmetric field theories and the refined BPS invariants of the dual geometries. In certain cases, this counting can also be mapped to the computation of degenerate conformal blocks in two-dimensional CFT’s. Degenerate limits of vertex operators in CFT receive a simple interpretation via geometric transitions in BPS counting.

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Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, 91125, USA

    Tudor Dimofte, Sergei Gukov & Lotte Hollands

  2. University of California, Santa Barbara, CA, 93106, USA

    Sergei Gukov & Lotte Hollands

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  1. Tudor Dimofte
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  2. Sergei Gukov
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  3. Lotte Hollands
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Dimofte, T., Gukov, S. & Hollands, L. Vortex Counting and Lagrangian 3-Manifolds. Lett Math Phys 98, 225–287 (2011). https://doi.org/10.1007/s11005-011-0531-8

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