Nature of the deconfining phase transition in the 2+1-dimensional SU(N) Georgi-Glashow model

TL;DR

This paper investigates the deconfining phase transition in the 2+1-dimensional SU(N) Georgi-Glashow model, showing it belongs to the Z_N universality class through a Coulomb gas and sine-Gordon model analysis.

Contribution

It demonstrates that the transition is governed by a generalized SU(N) sine-Gordon model with self-dual symmetry, leading to a Z_N parafermions conformal field theory at the infrared fixed point.

Findings

The phase transition is described by a Coulomb gas model of electric and magnetic charges.

The critical behavior aligns with a Z_N parafermions conformal field theory.

Supports the conjecture that the transition belongs to the Z_N universality class.

Abstract

The nature of the deconfining phase transition in the 2+1-dimensional SU(N) Georgi-Glashow model is investigated. Within the dimensional-reduction hypothesis, the properties of the transition are described by a two-dimensional vectorial Coulomb gas models of electric and magnetic charges. The resulting critical properties are governed by a generalized SU(N) sine-Gordon model with self-dual symmetry. We show that this model displays a massless flow to an infrared fixed point which corresponds to the Z$\_N$ parafermions conformal field theory. This result, in turn, supports the conjecture of Kogan, Tekin, and Kovner that the deconfining transition in the 2+1-dimensional SU(N) Georgi-Glashow model belongs to the Z$\_N$ universality class.