(2,2) Geometry from Gauge Theory

TL;DR

This paper uses gauge theory to construct and analyze generalized Kahler geometries with (2,2) supersymmetry, revealing new vacuum structures and dualities in these complex geometrical models.

Contribution

It introduces a method to construct generalized Kahler geometries via gauge theories and explores their vacuum structures, including cases with infinite supersymmetric vacua.

Findings

Construction of generalized Kahler geometries from gauge theories

Identification of T-dual squashed Kahler spaces

Discovery of models with infinite supersymmetric vacua

Abstract

Using gauge theory, we describe how to construct generalized Kahler 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 Kahler 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 Kahler dual descriptions possess unusual Coulomb branches. Specifically, there appear to be an infinite number of supersymmetric vacua.