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

2008/07/31 by Davide Gaiotto, Gregory W. Moore, Andrew Neitzke · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.DG

paper · pdf · doi:10.1007/s00220-010-1071-2

published as Commun.Math.Phys.299:163-224,2010 · 62 pages; v2: typos fixed, references added, minor improvements to exposition and notation; v3: typos fixed and small additions, including remark on TBA

arxiv created 2009/11/25 · arxiv updated 2014/11/18

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 R³ x 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.

Cited by

• Phase-locking in dynamical systems and quantum mechanics

Related

• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Wall-Crossing in Supersymmetric Gauge Theories
• Four-dimensional N=2 Field Theory and Physical Mathematics
• Crossing the Wall: Branes vs. Bundles
• Wall-crossing, Toric divisor and Seiberg duality