Liquid crystal defects and confinement in Yang-Mills theory

TL;DR

This paper explores topological defects like vortices and monopoles in SU(2) Yang-Mills theory within the Landau gauge, linking their proliferation to the confinement-deconfinement phase transition and quark confinement.

Contribution

It identifies and characterizes topological vortices and monopoles in Yang-Mills theory, proposing their role in the confinement mechanism and phase transition.

Findings

Existence of topological vortices similar to disclinations and Alice vortices.

Presence of monopoles analogous to defects in nematic crystals and liquid helium.

Proliferation of these defects correlates with deconfinement transition.

Abstract

We show that in the Landau gauge of the SU(2) Yang-Mills theory the residual global symmetry supports existence of the topological vortices which resemble disclination defects in the nematic liquid crystals and the Alice (half-quantum) vortices in the superfluid heluim 3 in the A-phase. The theory also possesses half-integer and integer charged monopoles which are analogous to the point-like defects in the nematic crystal and in the liquid helium. We argue that the deconfinement phase transition in the Yang-Mills theory in the Landau gauge is associated with the proliferation of these vortices and/or monopoles. The disorder caused by these defects is suggested to be responsible for the confinement of quarks in the low-temperature phase.