Phase Transition in Gauge Theories, Monopoles and the Multiple Point Principle

Abstract

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. Using renormalization group equations for the SM, the effective potential in the two-loop approximation is investigated, and the existence of its postulated second minimum at the fundamental scale is confirmed. Phase transitions in the lattice gauge theories are reviewed. The lattice results for critical coupling constants are compared with those of the Higgs monopole model, in which the lattice artifact monopoles are replaced by the point-like Higgs scalar particles with magnetic charge. Considering our (3 + 1)-dimensional space-time as, in some way, discrete or imagining it as a lattice with a parameter a = λ P , where λ P is the Planck length, we have investigated the additional contributions of monopoles to the β-functions of renormalization group equations for running fine structure constants α i (µ) (i = 1, 2, 3 correspond to the U (1), SU (2) and SU (3) gauge groups of the SM) in the FRGGM extended beyond the SM at high energies. It is shown that monopoles have N f am times smaller magnetic charge in the FRGGM than in the SM (N f am is a number of families in the FRGGM). We have estimated also the enlargement of a number of fermions in the FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have reviewed that, in contrast to the case of 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 possibility of the [SU (5)] 3 or [SO(10)] 3 unification at the GUT-scale ∼ 10 18 GeV is briefly considered.

New results at LHC confirming the vacuum stability and Multiple Point Principle

“…This problem is related with the concept of the Multiple Point Principle developed in Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17], presented in the book [18] and review [19], and with the problem of tiny value of cosmological constant and dark energy (see for example Refs. [15][16][17][20][21][22][23][24][25]).…”

Preon Model and Family Replicated E6 Unification

“…according to the MPP [9,10,11,12]. But at the scale M C our theory stops (it is not valid), and we do not know the development of our theory up to the Planck scale and further -in trans-Planckian region.…”

“…MPP postulates: all the vacua which might exist in Nature are degenerate and should have approximately zero vacuum energy density (cosmological constant). According to the MPP, there are two vacua in the SM (and its extension) with the same energy density, and all cosmological constants are zero or approximately zero [10,11] (see also review [12]) what is shown in Fig. 1.…”

MIRROR WORLD WITH BROKEN MIRROR PARITY, E6 UNIFICATION AND COSMOLOGY

“…But this problem is not trivially solved, and at present we have only a hypothesis. Now it is worth the reader's attention to observe that in the mirror world we have three scales (presumably corresponding to the three MPP vacua [87]):…”

“…The true Electroweak vacuum would have its vacuum energy density CC = ρ vac = 0. Such a scenario exists in the model with Multiple Point Principle (MPP) [82][83][84][85][86] (see also reviews [87,88] and references there). A non-zero (nevertheless tiny) CC would be associated only with a false vacuum.…”