Confinement in high-temperature lattice gauge theories

TL;DR

This paper explores the mechanisms of confinement in high-temperature SU(N) lattice gauge theories, emphasizing the role of monopoles and their analytical understanding through related spin models.

Contribution

It provides an analytical framework linking monopoles in lattice gauge theories to vortices in deformed spin models, enhancing understanding of confinement at high temperatures.

Findings

Monopoles are crucial for confinement in high-temperature gauge theories.

Vortices in XY models correspond to constituents of instantons in related models.

An effective U(1) description captures the confinement mechanism in SU(2) lattice gauge theory.

Abstract

There has been substantial progress in understanding a class of SU(N) gauge theories that are confining at high temperatures. This class includes theories with center-symmetric Polyakov loop deformations or with periodic adjoint fermions. The crucial role of monopoles in lattice gauge theories of this type can be understood analytically. The basic mechanisms occur in the two-dimensional O(3) spin model, deformed by appropriate mass term to give an XY model. Vortices of the XY model are constituents of O(3) instantons just as SU(N) magnetic monopoles are constituents of KvBLL instantons. Similar methods applied to an SU(2) lattice gauge theory yield an effective U(1) description in which monopoles are responsible for confinement.