Monopoles near the Planck Scale and Unification

Abstract

Considering our (3+1)-dimensional space-time as, in some way, discrete or l attice with a parameter $a={\lambda }_P$, where ${\lambda }_P$ is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to beta-functions of the renormalisation group equations for the running fine structure constants ${\alpha }_i(\mu )$ (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 al so 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 AntiGUT when the FRGGM undergoes the breakdown at $\mu ={\mu }_G\sim 10^{18}$ GeV, we have the possibility of unification if the FRGGM-breakdown occurs at ${\mu }_G\sim 10^{14}$ GeV. By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale ${\mu }_{GUT}\approx 10^{18.4}$ GeV. We discussed the possibility of $[SU(5){]}^3$ or $[SO(10){]}^3$ (SUSY or not SUSY) unifications.

49 pages, 7 figures

References in corpus (4)

• Family replicated gauge groups and large mixing angle solar neutrino solution
• Phase Transition Couplings in U(1) and SU(N) Regularized Gauge Theories
• Phase Transition in Gauge Theories and the Planck Scale Physics
• Multiple Point Model and Phase Transition Couplings in the Two-Loop Approximation of Dual Scalar Electrodynamics

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• Are Preons Dyons? Naturalness of Three Generations
• Family Replicated Gauge Group Models
• Seesaw scales and the steps from the Standard Model towards superstring-inspired flipped E_6
• Generalized dual symmetry of nonabelian theories and the freezing of α_s
• Duality-symmetric Action for Electromagnetic Theory with Electric and Magnetic Sources
• Quantum Gravity in Plebanski Formulation