Discrete gauge theories of charge conjugation

Understand

We define gauge theories whose gauge group includes charge conjugation as well as standard $\mathrm{SU}(N)$ transformations.

• When combined, these transformations form a novel type of group with a semidirect product structure.
• For $N$ even, we show that there are exactly two possible such groups which we dub $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$.
• We construct the transformation rules for the fundamental and adjoint representations, allowing us to explicitly build four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories based on $\widetilde{\mathrm{SU}}(N)_{\mathrm{I,II}}$ and understand from first principles their global symmetry.