New Topological Structures of Skyrme Theory: Baryon Number and Monopole Number

TL;DR

This paper reveals that skyrmions possess two independent topologies, leading to a classification scheme with two topological numbers, and shows the vacuum structure of Skyrme theory is analogous to combined features of Sine-Gordon theory and QCD.

Contribution

It introduces a novel classification of skyrmions using two topological numbers and links the vacuum structure of Skyrme theory to Sine-Gordon and QCD theories.

Findings

Skyrmions have two independent topologies: baryon and monopole.

Skyrmions are classified by two numbers (m,n), with baryon number B=mn.

The vacuum of Skyrme theory has a dual topological structure similar to Sine-Gordon and QCD.

Abstract

Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology $\pi_3(S^3)$ and the monopole topology $\pi_2(S^2)$. With this we propose to classify the skyrmions by two topological numbers $(m,n)$, the monopole number $m$ and the shell (radial) number $n$. In this scheme the popular (non spherically symmetric) skyrmions are classified as the $(m,1)$ skyrmions but the spherically symmetric skyrmions are classified as the $(1,n)$ skyrmions, and the baryon number $B$ is given by $B=mn$. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the Sine-Gordon theory and QCD combined together, which can also be classified by two topological numbers $(p,q)$. This puts the Skyrme theory in a totally new perspective.