| Summary: | Abstract We show that a new gauge group with one new scalar leads to automatically stable Dark Matter candidates. We consider theories where the Higgs phase is dual to the confined phase: it is known that SU (2) gauge theories with a scalar doublet (like the Standard Model) obey this non-trivial feature. We provide a general criterion, showing that this self-duality holds for SU(N), SO(N), Sp(N) and G2 gauge dynamics with a scalar field in the fundamental representation. The resulting Dark Matter phenomenology has non- trivial features that are characteristic of the group, and that we discuss case by case. Just to mention a few, SU(N) has an accidental conserved dark baryon number, SO (2N + 1) leads to stable glue-balls thanks to a special parity, G2 leads to a Dark Matter system analogous to neutral kaons. The cosmological Dark Matter abundance is often reproduced for masses around 100 TeV: all constraints are satisfied and lighter dark glue-balls can affect Higgs physics. These theories acquire additional interest and predictivity assuming that both the dark and weak scales are dynamically generated.
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