Deconfining Phase Transition in 2+1 D: the Georgi-Glashow Model

TL;DR

This study analyzes finite-temperature deconfinement in the 2+1D Georgi–Glashow model, showing the transition is governed by the restoration of the magnetic $Z_2$ symmetry and belongs to the 2D Ising universality class. By combining monopole-induced mass generation and charged-W plasma effects within a sine-Gordon–type RG framework, it demonstrates that neglecting the charged sector yields incorrect $T_c$ and universality, and it derives an explicit high-temperature effective action for the Polyakov loop. The work connects magnetic vortices to the Polyakov line and shows vortex correlators decay exponentially above the transition, consistent with symmetry restoration and deconfinement. These results illuminate the interplay between monopoles, vortices, and charged excitations, offering insights potentially relevant to higher-dimensional gauge theories including QCD.

Abstract

We analyze the finite temperature deconfining phase transition in 2+1 dimensional Georgi-Glashow model. We show explicitly that the transition is due to the restoration of the magnetic $Z_2$ symmetry and that it is in the Ising universality class. We find that neglecting effects of the charged $W$ bosons leads to incorrect predictions for the value of the critical temperature and the universality class of the transition, as well as for various correlation functions in the high temperature phase. We derive the effective action for the Polyakov loop in the high temperature phase and calculate the correlation functions of magnetic vortex operators.