8 - Nexuses, sphalerons, and fractional topological charge

Summary

Introduction to nexuses and junctions

So far, it may appear that center vortices are embedded Abelian objects. But center vortices can be extended to non-Abelian objects in several ways. We describe two: the first we call junctions, representing the merging and branching of vortex lines (or sheets, in d = 4) without the necessity of monopole-like objects called nexuses; the second are nexuses themselves, which are modifications of 't Hooft–Polyakov monopoles but with their magnetic flux bundled into tubes that are parts of center vortices. The most interesting property of nexuses is that, along with center vortices, they admit the formation of quantum lumps of nonintegral topological charge. Nexuses do not change the picture of confinement given in this book in any material way, although this is not completely obvious. But they enter in a crucial way into a reinterpretation of Polyakov's discussion of confinement in the d = 3 Georgi–Glashow model, as we indicate at the end of this section.

Note that we continue to use the notation of Chapter 7. All sections are in Euclidean space, except for Section 8.3.2, which is in Minkowski space.

Junctions

Junctions are thick points (d = 3) or lines (d = 4) where a vortex can branch into other vortices. It is easy to draw them in d = 3, where they look like vacuum Feynman graphs. Figure 8.1 shows a simple example with four junctions in SU(3), where three lines meet at each junction (up to N lines can meet at an SU(N) junction, each associated with a distinct flux matrix Q_j).