No-Go Theorem forSU(N)Unification of Extra-Strong Interactions

Abstract

It is shown that if dynamical symmetry breaking of weak interactions were due to an extra-strong $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ gauge interaction which is unified with quantum chromodynamics according to the simplest scheme it would contradict the behavior of coupling constants predicated by the renormalization group. This is proven first for any nonexotic irreducible representations of $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}\supset \mathrm{SU}\mathrm{}\left(3\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(1\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$; then it is argued that the theorem can be extended to any unifying simple Lie group.