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

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.

8 pages, 4 figures

References in corpus (3)

• States of Carbon-12 in the Skyrme Model
• Incarnations of Skyrmions
• A Skyrme model approach to the spin-orbit force

Cited by in corpus (2)

• Gravitational catalysis of merons in Einstein-Yang-Mills theory
• Skyrme-Faddeev Lagrangian from reformulated Georgi-Glashow model