Harland, D. orcid.org/0000-0002-4110-9673 and Sutcliffe, P.M. orcid.org/0000-0002-4713-4714 (Cover date: 20 October 2023) Rational Skyrmions. Journal of Physics A: Mathematical and Theoretical, 56 (42). 425401. ISSN 1751-8113
Abstract
A new method is introduced to construct approximations to Skyrmions that are explicit rational functions of the spatial Cartesian coordinates. The scheme uses ADHM data of a Yang-Mills instanton to produce a Skyrmion with a baryon number that is equal to the instanton number. The formula for the Skyrmion involves only the evaluation of the ADHM data, in contrast to the Atiyah-Manton construction that requires the solution of a differential equation that can only be solved explicitly in the case of a spherically symmetric Skyrmion. Examples with baryon numbers one and two are studied in detail. The energy of the rational Skyrmion with baryon number one is lower than that of the Atiyah-Manton Skyrmion, which is already within one percent of the energy of the true numerically computed Skyrmion. A family of baryon number two Skyrmions is presented, which includes an axially symmetric Skyrmion that smoothly transforms to a pair of well-separated single Skyrmions as the parameter is varied.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 The Author(s). Published by IOP Publishing Ltd. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
Keywords: | Skyrmions, ADHM construction, instantons |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Oct 2023 15:20 |
Last Modified: | 20 Sep 2024 00:13 |
Published Version: | https://iopscience.iop.org/article/10.1088/1751-81... |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1751-8121/acfbcc |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:203667 |
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