Monopoles, Vortices and Strings: Confinement and Deconfinement in 2+1 Dimensions at Weak Coupling

TL;DR

This paper explores the mechanisms of confinement and deconfinement in the 2+1 dimensional Georgi-Glashow model, analyzing monopoles, vortices, and strings, and examining the phase transition driven by magnetic symmetry restoration and string disintegration.

Contribution

It provides a comprehensive review of confinement and deconfinement mechanisms, including monopole plasma, vortex condensation, and the role of charged W bosons, with new insights into the phase transition dynamics.

Findings

Confinement arises from monopole plasma and vortex condensation.

Deconfinement involves magnetic symmetry restoration and W boson dynamics.

The phase transition is driven by string disintegration, not Hagedorn proliferation.

Abstract

We consider, from several complementary perspectives, the physics of confinement and deconfinement in the 2+1 dimensional Georgi-Glashow model. Polyakov's monopole plasma and 't Hooft's vortex condensation are discussed first. We then discuss the physics of confining strings at zero temperature. We review the Hamiltonian variational approach and show how the linear confining potential arises in this framework. The second part of this review is devoted to study of the deconfining phase transition. We show that the mechanism of the transition is the restoration of 't Hooft's magnetic symmetry in the deconfined phase. The heavy charged $W$ bosons play a crucial role in the dynamics of the transition, and we discuss the interplay between the charged $W$ plasma and the binding of monopoles at high temperature. Finally we discuss the phase transition from the point of view of confining strings. We show that from this point of view the transition is not driven by the Hagedorn mechanism (proliferation of arbitrarily long strings), but rather by the "disintegration" of the string due to the proliferation of 0 branes.