Mirror symmetry and Exact Solution of 4D N=2 Gauge Theories I

TL;DR

This paper provides exact solutions for the Coulomb branch moduli space of 4D N=2 gauge theories with product SU groups using geometric engineering, revealing novel geometric structures and strong coupling phenomena.

Contribution

It introduces a geometric engineering approach to solve the Coulomb branch of N=2 gauge theories with complex gauge group products and matter content, including new three-dimensional complex manifolds.

Findings

Exact solutions for Coulomb moduli spaces using geometric engineering

Identification of three-dimensional complex manifolds in certain cases

Discovery of new stringy strong coupling fixed points

Abstract

Using geometric engineering in the context of type II strings, we obtain exact solutions for the moduli space of the Coulomb branch of all N=2 gauge theories in four dimensions involving products of SU gauge groups with arbitrary number of bi-fundamental matter for chosen pairs, as well as an arbitrary number of fundamental matter for each factor. Asymptotic freedom restricts the possibilities to SU groups with bi-fundamental matter chosen according to ADE or affine ADE Dynkin diagrams. Many of the results can be derived in an elementary way using the self-mirror property of K3. We find that in certain cases the solution of the Coulomb branch for N=2 gauge theories is given in terms of a three dimensional complex manifold rather than a Riemann surface. We also study new stringy strong coupling fixed points arising from the compactification of higher dimensional theories with tensionless strings and consider applications to three dimensional N=4 theories.