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arXiv · 1509.08978

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

Y. M. Cho·Kyoungtae Kimm·J. H. Yoon·Pengming Zhang
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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 $π_3(S^3)$ and the monopole topology $π_2(S^2)$. 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.

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Y. M. Cho, Kyoungtae Kimm, J. H. Yoon, Pengming Zhang. 2017-01-23. New Topological Structures of Skyrme Theory: Baryon Number and Monopole Number. https://doi.org/10.1140/epjc%2Fs10052-017-4655-6

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