Reinterpretation of Faddeev-Niemi Knot in Skyrme Theory

TL;DR

This paper reinterprets the Faddeev-Niemi knot in Skyrme theory as a linked pair of quantized magnetic flux rings, offering new insights into the theory's potential applications in low energy physics.

Contribution

It provides a novel interpretation of the Faddeev-Niemi knot as linked magnetic flux rings in Skyrme theory, connecting topological properties to physical structures.

Findings

Faddeev-Niemi knot identified as a vortex ring of a helical baby skyrmion

Knot interpreted as two linked quantized magnetic flux rings

Linking number related to Chern-Simon index

Abstract

We identify the Faddeev-Niemi knot in Skyrme theory as a vortex ring made of a helical baby skyrmion (a twisted chromomagnetic vortex which is periodic in $z$-coodinate) with the periodic ends connected together. This allows us to interpret the knot as two quantized magnetic flux rings linked together, the first one winding the second $m$ times and the second one winding the first $n$ times, whose linking number $mn$ is fixed by the Chern-Simon index of the magnetic potential. This interpretation strongly suggests that the Skyrme theory could also describe a very interesting low energy physics in a completely different environment, which puts the theory in a totally new perspective.