Phase Transition in Gauge Theories and Multiple Point Model

TL;DR

This paper investigates phase transitions in U(1) gauge theories using a dual Abelian Higgs model, calculating critical couplings and comparing them with lattice results and the Multiple Point Model predictions near the Planck scale.

Contribution

It provides a two-loop approximation calculation of the critical coupling in U(1) gauge theory and compares it with lattice results and theoretical models.

Findings

Critical electric fine structure constant $oxed{ ext{approx. } 0.208}$ matches lattice results.

Phase transition behavior aligns with Multiple Point Model predictions.

Supports the existence of a multiple critical point at the Planck scale.

Abstract

In the present paper the phase transition in the regularized U(1) gauge theory is investigated using the dual Abelian Higgs model of scalar monopoles. The corresponding renormalization group improved effective potential, analogous to the Coleman-Weinberg's one, was considered in the two-loop approximation for $\beta$ functions, and the phase transition (critical) dual and non-dual couplings were calculated in the U(1) gauge theory. It was shown that the critical value of the renormalized electric fine structure constant $\alpha_{\text{crit}}\approx 0.208$ obtained in this paper coincides with the lattice result for compact QED: $\alpha_{\text{crit}}^{\text{lat}}\approx 0.20\pm 0.015$. This result and the behavior of $\alpha$ in the vicinity of the phase transition point were compared with the Multiple Point Model prediction for the values of $\alpha$ near the Planck scale. Such a comparison is very encouraging for the Multiple Point Model assuming the existence of the multiple critical point at the Planck scale.