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.
Highlights
Even though this construction may sound contrived, secretly, we are already familiar with it, since the good old O(2N ) groups can be regarded as the principal extension of SO(2N )
We introduce gauge theories based on a class of disconnected gauge groups, called principal extensions
In this work we focus on 4d theories with N = 2 SUSY, such construction is independent of spacetime dimensions and supersymmetry
Summary
We describe a family of Lie groups called the principal extensions [24], and describe some of their properties that are used in the rest of the paper. The principal extension of a connected and connected Lie group G is a disconnected group G whose connected component is G and whose group of connected components G/G is isomorphic to the group of automorphisms of the Dynkin diagram of G. Because of this definition the cases of interest, where G = G, correspond to Dynkin diagrams with non-trivial automorphisms.
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