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

Davide Gaiotto, Gregory W. Moore, Andrew Neitzke

Research output: Contribution to journalArticlepeer-review

220 Scopus citations


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 ℝ3 × S1. 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.

Original languageEnglish (US)
Pages (from-to)163-224
Number of pages62
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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