https://doi.org/10.1140/epjc/s10052-017-4655-6
Regular Article - Theoretical Physics
New topological structures of Skyrme theory: baryon number and monopole number
1
Institute of Modern Physics, Chinese Academy of Science, Lanzhou, 730000, China
2
Konkuk University, Administration Building 310-4, Seoul, 143-701, Korea
3
School of Physics and Astronomy, Seoul National University, Seoul, 151-742, Korea
4
Faculty of Liberal Education, Seoul National University, Seoul, 151-747, Korea
5
Department of Physics, Konkuk University, Seoul, 143-701, Korea
* e-mail: ymcho7@konkuk.ac.kr
Received:
1
March
2016
Accepted:
26
January
2017
Published online:
9
February
2017
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 
and the monopole topology 
. 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 
. 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.
© The Author(s), 2017
