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Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory

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Abstract

We give a physical explanation of the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum in Seiberg-Witten theories. In the process we give an exact description of the BPS instanton corrections to the hyperkähler metric of the moduli space of the theory on \({\mathbb R^3 \times S^1}\). The wall-crossing formula reduces to the statement that this metric is continuous. Our construction of the metric uses a four-dimensional analogue of the two-dimensional tt* equations.

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Authors and Affiliations

  1. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Davide Gaiotto & Andrew Neitzke

  2. NHETC and Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, 08855–0849, USA

    Gregory W. Moore

Authors
  1. Davide Gaiotto
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  2. Gregory W. Moore
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  3. Andrew Neitzke
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Correspondence to Andrew Neitzke.

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Communicated by A. Kapustin

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Gaiotto, D., Moore, G.W. & Neitzke, A. Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory. Commun. Math. Phys. 299, 163–224 (2010). https://doi.org/10.1007/s00220-010-1071-2

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