  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 G_2 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, G_2 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.
