@article{c461bdbd460b4acfbb1324a22aec3917,

title = "Linking number of vortices as baryon number",

abstract = "We show that the topological degree of a Skyrmion field is the same as the Hopf charge of the field under the Hopf map and thus equals the linking number of the preimages of two points on the 2-sphere under the Hopf map. We further interpret two particular points on the 2-sphere as vortex zeros and the linking of these zero lines follows from the latter theorem. Finally we conjecture that the topological degree of the Skyrmion can be interpreted as the product of winding numbers of vortices corresponding to the zero lines, summing over clusters of vortices.",

author = "Gudnason, {Sven Bjarke} and Muneto Nitta",

note = "Funding Information: We would like to thank Michikazu Kobayashi for collaboration at the early stage of this work and we thank Chris Halcrow, Steffen Krusch, Martin Speight, and Paul Sutcliffe for discussions and comments. S. B. G. thanks the Outstanding Talent Program of Henan University for partial support. The work of S. B. G. is supported by the National Natural Science Foundation of China (Grant No. 11675223). M. N. is supported by the Ministry of Education, Culture, Sports, Science (MEXT)-Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006) and by a Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” (KAKENHI Grant No. 15H05855) from MEXT, Japan. M. N. is also supported in part by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI Grant No. 16H03984 and No. 18H01217). Publisher Copyright: {\textcopyright} 2020 authors. Published by the American Physical Society.",

year = "2020",

month = mar,

day = "15",

doi = "10.1103/PhysRevD.101.065011",

language = "English",

volume = "101",

journal = "Physical Review D",

issn = "2470-0010",

publisher = "American Physical Society",

number = "6",

}