The Problem of Monopoles in the Standard and Family Replicated Models

The aim of the present talk is to show that monopoles cannot play any role in the Standard Model (SM), and in its usual extensions, up to the Planck scale: M Pl = 1 . 22 · 10 19 GeV, because they have a huge charge and are completely confined or screened. The possibility of the extension of the SM with a Family Replicated Gauge Group (FRGG) symmetry of the type ( SMG ) N = [ SU (3) c ] N × [ SU (2) L ] N × [ U (1) Y ] N is briefly discussed. It was shown that the Abelian monopoles (existing also in non-Abelian theories) in FRGG model have N ∗ times smaller magnetic charge than in the SM, where N ∗ = N ( N + 1) / 2. These monopoles can appear at the high energies in the FRGG-model and give additional contributions to the beta–functions of the renormalisation group equations for the running constants α i ( µ ), where i=1,2,3 correspond to the U(1), SU(2) and SU(3) gauge groups of the SM.