Nexus solitons in the center vortex picture of QCD

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 $\mathrm{SU}\mathrm{}\left(N\right),$ up to N vortices meet at a center, or nexus, provided that the total flux of the vortices adds to zero (mod $N).\mathrm{}$ There are fundamentally two kinds of nexuses: Quasi-Abelian, which can be described as composites of Abelian embedded 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 $\mathrm{SU}\mathrm{}\left(2\right).$ 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.