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

Gauge theories from principally extended disconnected gauge groups