(2, 2) geometry from gauge theory

Abstract

Using gauge theory, we describe how to construct generalized Kähler geometries with (2, 2) two-dimensional supersymmetry, which are analogues of familiar examples like projective spaces and Calabi-Yau manifolds. For special cases, T-dual descriptions can be found which are squashed Kähler spaces. We explore the vacuum structure of these gauge theories by studying the Coulomb branch, which usually encodes the quantum cohomology ring. Some models without Kähler dual descriptions possess unusual Coulomb branches. Specifically, there appear to be an infinite number of supersymmetric vacua.