Monopoles and Family Replicated Unification
  The present theory is based on the assumption that at the very small (Planck scale) distances our space-time is discrete, and this discreteness influences on the Planck scale physics. Considering our (3+1)-dimensional space-time as a regular hypercubic lattice with a parameter $a=\lambda_\text{P}$, where $\lambda_\text{P}$ is the Planck length, we have investigated a role of lattice artifact monopoles which is essential near the Planck scale if the Family replicated gauge group model (FRGGM) is an extension of the Standard Model at high energies. It was shown that monopoles have $N$ times smaller magnetic charge in FRGGM than in SM ($N$ is the number of families in FRGGM). These monopoles can give an additional contribution to beta-functions of the renormalisation group equations for the running fine structure constants $\alpha_\text{i}(\mu)$ (i=1,2,3 correspond to the U(1), SU(2), and SU(3) gauge groups of the Standard Model). We have used the Dirac relation for renormalised electric and magnetic charges. Also we have estimated the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. Different role of monopoles in the vicinity of the Planck scale gives rise or to AntiGUT, or to the new possibility of unification of gauge interactions (including gravity) at the scale $\mu_\text{GUT}\approx 10^{18.4}$ GeV. We discussed the possibility of the [SU(5)]$^3$ SUSY or [SO(10)]$^3$ SUSY unifications. 
L. V. Laperashvili (ITEP, Moscow, Russia), H. B. Nielsen (NBI,   Copenhagen, Denmark) D. A. Ryzhikh (ITEP, Moscow, Russia)