Supersymmetric Gauge Theory, Wall-Crossing and Hyperkähler Geometry

Abstract

In this thesis we study moduli spaces of four-dimensional N = 2 supersymmetric gauge theories. We focus on the vector multiplet moduli space and describe how the rigid special geometry of the Coulomb branch determines the couplings in the effective Lagrangian. Compactication to three dimensions gives rise to an N = 4 theory whose moduli space is hyperkähler. The twistor space construction of this hyperkähler metric is presented and put in the context of Gaiotto, Moore and Neitzke's physical interpretation of the solution by Kontsevich and Soibelman of the wall-crossing problem.