Details
| Original language | English |
|---|---|
| Pages (from-to) | 3944-3990 |
| Number of pages | 47 |
| Journal | NONLINEARITY |
| Volume | 35 |
| Issue number | 8 |
| Early online date | 23 Jun 2022 |
| Publication status | Published - 4 Aug 2022 |
Abstract
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.
Keywords
- 14D21, 53C29, 70S15, 70S20, instantons, Skyrme model, skyrmions, topological solitons
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Mathematics(all)
- Applied Mathematics
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In: NONLINEARITY, Vol. 35, No. 8, 04.08.2022, p. 3944-3990.
Research output: Contribution to journal › Article › Research › peer review
}
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 -