Four-dimensional wall-crossing via three-dimensional field theory

Details Four-dimensional wall-crossing via three-dimensional field theory Four-dimensional wall-crossing via three-dimensional field theory

2008-07-29

arxiv.org/abs/0807.4723v3

Physics

High Energy Physics

High Energy Physics - Theory

62 pages; v2: typos fixed, references added, minor improvements to exposition and notation; v3: typos fixed and small addition

Scientific paper

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 hyperkahler metric of the moduli space of the theory on R^3 x 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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