Phase transition in gauge theories, monopoles and the Multiple Point Principle

This review is devoted to the Multiple Point Principle (MPP), according to which several vacuum states with the same energy density exist in Nature. The MPP is implemented to the Standard Model (SM), Family replicated gauge group model (FRGGM) and phase transitions in gauge theories with/without monopoles. Lattice gauge theories are reviewed. The lattice results for critical coupling constants are compared with those of the Higgs Monopole Model (HMM), in which the lattice artifact monopoles are replaced by the point-like Higgs scalar particles with a magnetic charge. Considering our (3+1)-dimensional space-time as discrete, for example, as a lattice with a parameter a=\lambda_P, equal to the Planck length, we have investigated the additional contributions of monopoles to beta-functions of renormalization group equations in the FRGGM extended beyond the SM at high (the Planck scale) energies. We have reviewed that, in contrast to the Anti-grand unified theory (AGUT), there exists a possibility of unification of all gauge interactions (including gravity) near the Planck scale due to monopoles. The unifications [SU(5)]^3 and [SO(10)]^3 at the GUT-scale \sim 10^{18} GeV are briefly discussed.