Gauge theories from principally extended disconnected gauge groups

TL;DR

This paper introduces gauge theories based on disconnected gauge groups called principal extensions, exploring their structure, physical implications, and how they modify Coulomb and Higgs branch properties in supersymmetric theories.

Contribution

It presents a novel class of gauge theories with disconnected groups, extending the concept of discrete charge conjugation gauging to arbitrary ranks and analyzing their physical consequences.

Findings

Coulomb branch is generically non-freely generated.

Global symmetry of the Higgs branch is modified.

Construction is independent of spacetime dimensions and supersymmetry.

Abstract

We introduce gauge theories based on a class of disconnected gauge groups, called principal extensions. Although in this work we focus on 4d theories with N=2 SUSY, such construction is independent of spacetime dimensions and supersymmetry. These groups implement in a consistent way the discrete gauging of charge conjugation, for arbitrary rank. Focusing on the principal extension of SU(N), we explain how many of the exact methods for theories with 8 supercharges can be put into practice in that context. We then explore the physical consequences of having a disconnected gauge group: we find that the Coulomb branch is generically non-freely generated, and the global symmetry of the Higgs branch is modified in a non-trivial way.