Multiple Model of Anti-Grand Unification, The Regularization with Wilson Loop Action and Critical Coupling Constants

Abstract

The present work considers the phase transition between the confinement and "Coulomb" phases in U(1) gauge theory described by Wilson loop action. It was shown (using as an example the approximation of circular loops) that the critical coupling constant is rather independent of the regularization method. Taking into account the renormalization by artefact monopole contributions and the existence of strings in confinement phase assuming the maximal value of the effective fine structure constant equal to α max =π/12≈0.26, we obtain α c ≈0.204, in agreement with Monte Carlo lattice simulation result: α c ≈0.20. Such an approximate regularization independence ("universality") of the critical couplings is needed for the fine structure constant predictions claimed from "the multiple-point criticality principle".

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

“…The purpose was to investigate this approximate stability of the critical coupling with respect to a somewhat new regularization being used instead of the lattice, rather than just modifying the lattice in various ways. In [20] the Wilson loop action was considered in the approximation of circular loops of radii R ≥ a. It was shown that the phase transition coupling constant is indeed approximately independent of the regularization method: α crit ≈ 0.204, in correspondence with the Monte Carlo simulation result on lattice: α crit ≈ 0.20 ± 0.015 (see Eq.…”

“…In the Anti-grand unified theory (AGUT) [11][12][13][14][15][16][17][18][19][20][21] the FRGG breakdown was considered at µ G ∼ 10 18 GeV. It is a significant point for MPM.…”

“…[11,12] as an extension of the SM (see also reviews [13,14]), fits the SM fermion masses and mixing angles and describes all neutrino experimental data order of magnitude-wise using only 5 free parameters -five vacuum expectation values of the Higgs fields which break the FRGG symmetry to the SM. This approach based on the FRGG-model was previously called Anti-Grand Unified Theory (AGUT) and developed as a realistic alternative to SUSY Grand Unified Theories (GUTs) [11][12][13][14][15][16][17][18][19][20][21]. In Refs.…”

Phase transition in gauge theories and multiple-point model

“…The philosophy of the Multiple Point Model (MPM) suggested in [1] and developed in [2][3][4] leads to the necessity to investigate the phase transition in different gauge theories.…”

“…Monte Carlo simulations of these simple Wilson lattice theories in the four dimensions showed a (or an almost) second-order deconfining phase transition for U (1) [6,7], a crossover behavior for SU (2) and SU (3) [8,9], and a first-order phase transition for SU (N) with N ≥ 4 [10]. Bhanot and Creutz [11,12] have generalized the simple Wilson action, introducing two parameters in action:…”