TY - JOUR

T1 - ADHM skyrmions

AU - Cork, Josh

AU - Halcrow, Chris

N1 - Funding Information: The authors have benefited greatly from the lively online communities which arose over the last couple of years, including the Scheme 3 London Mathematical Society lectures on solitons, and the ongoing solitons at work network. Special thanks should also go to Derek Harland for many helpful conversations regarding the ideas and results of this paper. While this work was completed, CH was supported by The Leverhulme Trust as an Early Career Fellow and by the University of Leeds as an Academic Development Fellow.

PY - 2022/8/4

Y1 - 2022/8/4

N2 - We propose, via the Atiyah-Manton approximation, a framework for studying skyrmions on R3 using Atiyah-Drinfeld-Hitchin-Manin (ADHM) data for Yang-Mills instantons on R4. We provide a dictionary between important concepts in the Skyrme model and analogous ideas for ADHM data, and describe an efficient process for obtaining approximate Skyrme fields directly from ADHM data. We show that the approximation successfully describes all known skyrmions with charge B≤8, with energies reproduced within 2% of the true minimisers. We also develop factorisation methods for studying clusters of instantons and skyrmions, generalising early work by Christ-Stanton-Weinberg, and describe some relatively large families of explicit ADHM data. These tools provide a unified framework for describing coalesced highly-symmetric configurations as well as skyrmion clusters, both of which are needed to study nuclear systems in the Skyrme model.

AB - We propose, via the Atiyah-Manton approximation, a framework for studying skyrmions on R3 using Atiyah-Drinfeld-Hitchin-Manin (ADHM) data for Yang-Mills instantons on R4. We provide a dictionary between important concepts in the Skyrme model and analogous ideas for ADHM data, and describe an efficient process for obtaining approximate Skyrme fields directly from ADHM data. We show that the approximation successfully describes all known skyrmions with charge B≤8, with energies reproduced within 2% of the true minimisers. We also develop factorisation methods for studying clusters of instantons and skyrmions, generalising early work by Christ-Stanton-Weinberg, and describe some relatively large families of explicit ADHM data. These tools provide a unified framework for describing coalesced highly-symmetric configurations as well as skyrmion clusters, both of which are needed to study nuclear systems in the Skyrme model.

KW - 14D21

KW - 53C29

KW - 70S15

KW - 70S20

KW - instantons

KW - Skyrme model

KW - skyrmions

KW - topological solitons

UR - http://www.scopus.com/inward/record.url?scp=85134684036&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2110.15190

DO - 10.48550/arXiv.2110.15190

M3 - Article

AN - SCOPUS:85134684036

VL - 35

SP - 3944

EP - 3990

JO - NONLINEARITY

JF - NONLINEARITY

SN - 0951-7715

IS - 8

ER -