N=1 Dualities for Exceptional Gauge Groups and Quantum Global Symmetries

TL;DR

This paper explores dualities in N=1 supersymmetric gauge theories with exceptional groups, revealing hidden quantum global symmetries that emerge in the dual descriptions, especially using self-dual models for specific matter content.

Contribution

It extends known dualities to exceptional gauge groups and uncovers phenomena where global symmetries are hidden on the magnetic side, not manifest in the Lagrangian.

Findings

Dual pairs derived for exceptional groups like E7, E6, F4.

Full global symmetry often hidden on the magnetic side.

Construction of duals for special matter content.

Abstract

We discuss our attempts to generalize the known examples of dualities in N=1 supersymmetric gauge theories to exceptional gauge groups. We derive some dual pairs from known examples connected to exceptional groups and find an interesting phenomenon: sometimes the full global symmetry is ``hidden'' on the magnetic side. It is not realized as a symmetry on the fundamental fields in the Lagrangian. Rather, it emerges as a symmetry of the quantum theory. We then focus on an approach based on self-dual models. We construct duals for some very special matter content of $E_ 7$, $E_6$ and $F_4$. Again we find that the full global symmetry is not realized on the fundamental fields.