Extended-natural gauge models and complementarity

We propose a new condition “extended naturalness” which should be satisfied by any physically sensible gauge theory. In order that a theory is extended-natural, all discrete quantities observed in low energies must be stable against variations of discrete parameters of the theory defined in large mass scales. We find that SU(N) gauge models become extended-natural when we choose appropriate fermion representations. Further, if N is a multiple of 8, the models turn out to be good examples of complementary gauge theories.