Non-maximal and disconnected stability groups: SU(3) counter-example to Michel conjecture

Abstract It is now known that, for the first- and second-rank tensor representations of SU( n ) and O( n ), the stability subgroups for renormalizable Higgs potentials are maximal and are connected (modulo the Z 2 of O( n )). In this note, a first step beyond these standard representations is taken by considering the (2,2) (fourth-rank tensor) representation of SU(3). It is shown that in this case the stability subgroups need not be either maximal (thus furnishing a counter-example to the Michel conjecture) or connected (thus possibly providing a mechanism for discrete horizontal symmetry).