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Rational Skyrmions

Harland, Derek; Sutcliffe, Paul

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Derek Harland


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.


Harland, D., & Sutcliffe, P. (2023). Rational Skyrmions. Journal of Physics A: Mathematical and Theoretical, 56(42), Article 425401.

Journal Article Type Article
Acceptance Date Sep 20, 2023
Online Publication Date Sep 29, 2023
Publication Date Oct 20, 2023
Deposit Date Sep 30, 2023
Publicly Available Date Oct 2, 2023
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 56
Issue 42
Article Number 425401
Public URL


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