Confinement, brane symmetry and the Julia-Toulouse approach for condensation of defects

TL;DR

This paper explores charge confinement in Abelian gauge theories via brane symmetry breaking, using a generalized Julia-Toulouse approach to describe defect condensation and its implications for confinement regimes.

Contribution

It introduces a generalized Julia-Toulouse method compatible with Elitzur's theorem for describing defect condensation and confinement in gauge theories.

Findings

Universal criterion for charge confinement via brane symmetry breaking.

Generalized Julia-Toulouse approach for defect condensation.

Applications demonstrating the method's effectiveness.

Abstract

In this work the phenomenon of charge confinement is approached in various contexts. An universal criterion for the identification of this phenomenon in Abelian gauge theories is suggested: the so-called spontaneous breaking of the brane symmetry. This local symmetry has its most common manifestation in the Dirac string ambiguity present in the electromagnetic theory with monopoles. The spontaneous breaking of the brane symmetry means that the Dirac string becomes part of a brane invariant observable which hides the realization of such a symmetry and develops energy content in the confinement regime. The establishment of this regime can be reached through the condensation of topological defects. The effective theory of the confinement regime can be obtained with the Julia-Toulouse prescription which (originally introduced as the dual mechanism to the Abelian Higgs Mechanism) is generalized in this paper in order to become fully compatible with Elitzur's theorem and describe more general condensates which may break Lorentz and discrete spacetime symmetries. This generalized approach for the condensation of defects is presented here through a series of different applications.