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

P Lecheminant

doi:10.1016/j.physletb.2006.12.079

Abstract

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.

Highlights

The 2+1 dimensional Georgi Glashow (GG) model has attracted a lot of interest in the past since it is a much simpler theory than QCD but still retains some common interesting features like the existence of a confinement phase
Where S xi, gαi; yj, eαj is the effective action of M monopoles located at xi with magnetic charges gαi, fugacity ζαi and N W bosons at positions yj with electric charges eαj, fugacity ζαj
The Gaussian self-dual symmetry Φ ↔ Θ coincides to the Kramers-Wannier (KW) duality symmetry of the Ising model associated to the Majorana fermion ξ1: no mass term iξR1 ξL1, which is odd under the KW duality, can appear in the effective Hamiltonian

Summary

Introduction

The 2+1 dimensional Georgi Glashow (GG) model has attracted a lot of interest in the past since it is a much simpler theory than QCD but still retains some common interesting features like the existence of a confinement phase. The partition function, which describes the two-dimensional vectorial Coulomb gas of monopoles and massive gauge bosons, reads as follows: Z. where S xi, gαi; yj, eαj is the effective action of M monopoles located at xi with magnetic charges gαi, fugacity ζαi and N W bosons at positions yj with electric charges eαj , fugacity ζαj. The low-energy theory reduces to a sineGordon model for the Φ field and a mass-gap is induced It corresponds to the confinement phase where the massive W gauge bosons can be neglected. This self-dual symmetry is realized when ζ = ζand T = g2/4π In this case, the confinement-deconfinement transition is governed by the SU(N) SDSG model (1).

Ising criticality

Z3 criticality

The general case