Exceptional Equivalences in N=2 Supersymmetric Yang-Mills Theory

TL;DR

This paper discovers low energy equivalences between different N=2 supersymmetric gauge theories, including exceptional groups, using subgroup constructions, and solves specific theories within this framework.

Contribution

It introduces a method to establish equivalences between N=2 theories with various gauge groups, including exceptional ones, expanding understanding of their low energy dynamics.

Findings

Identified equivalences between theories with different gauge groups.

Constructed equivalences based on subgroup structures.

Solved specific G2, F4, and E6 theories using these methods.

Abstract

We find low energy equivalences between $N=2$ supersymmetric gauge theories with different simple gauge groups with and without matter. We give a construction of equivalences based on subgroups and find all examples with maximal simple subgroups. This is used to solve some theories with exceptional gauge groups $G_2$ and $F_4$. We are also able to solve an $E_6$ theory on a codimension one submanifold of its moduli space.