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