Solution of N=2 Gauge Theories via Compactification to Three Dimensions

TL;DR

This paper introduces an alternative method to analyze certain N=2 gauge theories by compactifying to three dimensions and using mirror symmetry, connecting brane configurations to integrable systems like Hitchin systems.

Contribution

It presents a novel approach to solving elliptic N=2 gauge theories through compactification and mirror symmetry, avoiding M-theory lift complexities.

Findings

Exact analysis of Coulomb and Higgs branches.

Mapping of gauge theories to Hitchin integrable systems.

Simplification of brane configurations using D-branes.

Abstract

A number of N=2 gauge theories can be realized by brane configurations in Type IIA string theory. One way of solving them involves lifting the brane configuration to M-theory. In this paper we present an alternative way of analyzing a subclass of these theories (elliptic models). We observe that upon compactification on a circle one can use a version of mirror symmetry to map the original brane configuration into one containing only D-branes. Simultaneously the Coulomb branch of the four-dimensional theory is mapped to the Higgs branch of a five-dimensional theory with three-dimensional impurities. The latter does not receive quantum corrections and can be analyzed exactly. The solution is naturally formulated in terms of an integrable system, which is a version of a Hitchin system on a punctured torus.