Nexus solitons in the center vortex picture of QCD

TL;DR

This paper explores nexus solitons in the center vortex model of QCD, identifying two types—quasi-Abelian and non-Abelian—and discusses their potential impact on the understanding of the QCD vacuum and confinement.

Contribution

It introduces and analyzes the concept of nexus solitons in the center vortex picture of QCD, including analytic solutions for quasi-Abelian cases and variational estimates for non-Abelian cases.

Findings

Nexus solitons can be classified into quasi-Abelian and non-Abelian types.

Analytic solutions exist for quasi-Abelian nexus solitons.

Non-Abelian nexus solitons carry topological charge and may modify the QCD vacuum picture.

Abstract

It is very plausible that confinement in QCD comes from linking of Wilson loops to finite-thickness vortices with magnetic fluxes corresponding to the center of the gauge group. The vortices are solitons of a gauge-invariant QCD action representing the generation of gluon mass. There are a number of other solitonic states of this action. We discuss here what we call nexus solitons, in which for gauge group SU(N), up to N vortices meet a a center, or nexus, provided that the total flux of the vortices adds to zero (mod N). There are fundamentally two kinds of nexuses: Quasi-Abelian, which can be described as composites of Abelian imbedded monopoles, whose Dirac strings are cancelled by the flux condition; and fully non-Abelian, resembling a deformed sphaleron. Analytic solutions are available for the quasi-Abelian case, and we discuss variational estimates of the action of the fully non-Abelian nexus solitons in SU(2). The non-Abelian nexuses carry Chern-Simons number (or topological charge in four dimensions). Their presence does not change the fundamentals of confinement in the center-vortex picture, but they may lead to a modified picture of the QCD vacuum.