Exact Results in D=2 Supersymmetric Gauge Theories

TL;DR

This paper computes exact partition functions for 2D N=(2,2) supersymmetric gauge theories on S^2, revealing dual descriptions, connections to Liouville/Toda CFT, and evidence for Seiberg duality, with implications for Calabi-Yau sigma models.

Contribution

It provides exact results for the S^2 partition function, linking gauge theories to conformal field theories and demonstrating dualities and topology-changing transitions.

Findings

Partition function admits Coulomb branch and vortex sum representations.

Correlation functions in Liouville/Toda CFT compute the gauge theory partition function.

Partition functions of Seiberg dual pairs are identical.

Abstract

We compute exactly the partition function of two dimensional N=(2,2) gauge theories on S^2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and anti-vortex excitations on the Higgs branches of the theory. We further demonstrate that correlation functions in two dimensional Liouville/Toda CFT compute the S^2 partition function for a class of N=(2,2) gauge theories, thereby uncovering novel modular properties in two dimensional gauge theories. Some of these gauge theories flow in the infrared to Calabi-Yau sigma models - such as the conifold - and the topology changing flop transition is realized as crossing symmetry in Liouville/Toda CFT. Evidence for Seiberg duality in two dimensions is exhibited by demonstrating that the partition function of conjectured Seiberg dual pairs are the same.