Communications in Mathematical Physics

, Volume 299, Issue 1, pp 163–224 | Cite as

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

  • Davide Gaiotto
  • Gregory W. Moore
  • Andrew NeitzkeEmail author


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.


Gauge Theory Wilson Line Marginal Stability Coulomb Branch Irregular Singularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Davide Gaiotto
    • 1
  • Gregory W. Moore
    • 2
  • Andrew Neitzke
    • 1
    Email author
  1. 1.School of Natural SciencesInstitute for Advanced StudyPrincetonUSA
  2. 2.NHETC and Department of Physics and AstronomyRutgers UniversityPiscatawayUSA

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