I will show that a new gauge group with one new scalar leads to automatically stable Dark Matter candidates. This stems from an intriguing field-theoretical duality between the Higgs and the confined phase of several gauge theories with a scalar in the fundamental representation. The resulting Dark Matter phenomenology has non-trivial features that are characteristic of the group. 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, without any tension with existing bounds, contrary to many other thermal candidates.
