MONOPOLES NEAR THE PLANCK SCALE AND UNIFICATION

Abstract

Considering our (3+1)-dimensional space–time as, in some way, discrete or lattice with a parameter a = λP, where λP is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to beta functions of the renormalization group equations for the running fine structure constants αi(μ) (i = 1,2,3 correspond to the U(1), SU(2) and SU(3) gauge groups of the Standard Model) in the Family Replicated Gauge Group Model (FRGGM) which is an extension of the Standard Model at high energies. It was shown that monopoles have N fam times smaller magnetic charge in FRGGM than in SM (N fam is the number of families in FRGGM). We have estimated also the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have shown that, in contrast to the case of anti-GUT when the FRGGM undergoes the breakdown at μ = μG ~ 1018 GeV , we have the possibility of unification if the FRGGM-breakdown occurs at μG ~ 1014 GeV . By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale μ GUT ≈ 1018.4 GeV . We discussed the possibility of [ SU (5)]3 or [ SO (10)]3 (SUSY or not SUSY) unifications.