Monopoles near the Planck Scale and Unification

TL;DR

This paper investigates how lattice artifact monopoles near the Planck scale influence gauge coupling unification in an extended Standard Model framework, suggesting unification at around 10^{18.4} GeV with potential GUT groups.

Contribution

It introduces the effects of lattice artifact monopoles on beta-functions in the Family Replicated Gauge Group Model and explores unification scenarios at high energies.

Findings

Monopoles have reduced magnetic charge in FRGGM compared to SM.

Unification of all gauge interactions including gravity is possible at ~10^{18.4} GeV.

Unification may involve [SU(5)]^3 or [SO(10)]^3 groups, with or without SUSY.

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.