Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
3D N=4 Supersymmetric Gauge Theories and Hyperk¨ahler Metrics
Friday, October 17th, 2008, 4:00 p.m.
Room 6635 South Hall
Abstract: Seiberg and Witten famously determined the dynamics of four dimensional
gauge theories with N=2 supersymmetry using constraints from low energy effective
field theory. Compactification to three dimensions yields a sigma model with N=4
supersymmetry and a hyperk¨ahler manifold as its target space. We describe how
the spectrum of BPS instantons is encoded in the hyperk¨ahler metric and Hitchin's
construction of hyperk¨ahler metrics using twistor methods. These techniques provide
the foundation for Gaiotto, Moore, and Neitzke's recent work on the Kontsevich-
Soibelman wall-crossing formula for BPS degeneracies.
Information about future meetings of this seminar can be found at