Unification

Abstract

Shortly after the SM was established and asymptotic freedom realized, it was suggested that the SM semi-simple product group of SU(3) × SU(2) × U(l) is embedded at some high energies in a unique simple group, for example SU(5) (which like the SM group has rank 5 and hence is the smallest simple group that can contain the SM gauge structure). Aside from implications for quark-lepton unification, Higgs fields, and the proton stability (to which we will return) it predicts first and foremost that the seemingly independent SM gauge couplings originate from a single coupling of the unified simple group [80] and that their infrared splitting is therefore due to only the scaling (or renormalization) of the corresponding quantum field theory from high to low energies [81]. Independently, it was also realized in the context of string theory that the theory just below the string scale often (but not always) has a unique (or unified) value for all gauge couplings [19, 18, 82, 83], regardless of whether the SM group itself truly unifies (in the sense of (i) embedding all SM fields in representations of some simple group, and (ii) spontaneous breaking of that group).