English

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

High Energy Physics - Theory 2014-11-18 v3 Differential Geometry

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 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.

Keywords

Cite

@article{arxiv.0807.4723,
  title  = {Four-dimensional wall-crossing via three-dimensional field theory},
  author = {Davide Gaiotto and Gregory W. Moore and Andrew Neitzke},
  journal= {arXiv preprint arXiv:0807.4723},
  year   = {2014}
}

Comments

62 pages; v2: typos fixed, references added, minor improvements to exposition and notation; v3: typos fixed and small additions, including remark on TBA

R2 v1 2026-06-21T11:05:35.457Z