ADHM skyrmions

Abstract

We propose, via the Atiyah-Manton approximation, a framework for studying skyrmions on ${\mathbb{R}}^3$ using ADHM data for Yang-Mills instantons on ${\mathbb{R}}^4$. 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. We show that the approximation successfully describes all known skyrmions with charge $\mathcal{B}\le 8$, 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.

arXiv comment50 pages, 7 figures

References in corpus (29)

• Low energy hadron physics in holographic QCD
• Skyrmions, instantons and holography
• Solitonic fullerene structures in light atomic nuclei
• Light Nuclei as Quantized Skyrmions
• A dynamical $\alpha$-cluster model of ${}^{16}$O
• Skyrmions up to Baryon Number 108
• Attractive Channel Skyrmions and the Deuteron
• Vibrational quantisation of the B=7 Skyrmion
• Quantising the B=2 and B=3 Skyrmion systems
• Zero mode quantization of multi-Skyrmions
• Monopole Scattering with a Twist
• Skyrmions, instantons, mass and curvature
• Vibrational modes of Skyrmions
• Symmetric Instantons and Skyrme Fields
• An Alpha Particle Model for Carbon-12
• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• Symmetric Calorons
• Instantons and the Buckyball
• A Smörgåsbord of Skyrmions
• Instanton vibrations of the 3-Skyrmion
• A model for gauged skyrmions with low binding energies
• The low energy dynamics of charge two dyonic instantons
• Coriolis terms in Skyrmion Quantization
• Skyrmion Vibration Modes within the Rational Map Ansatz
• Symmetric hyperbolic monopoles
• A consistent two-skyrmion configuration space from instantons
• Skyrmions from calorons
• ADHM Polytopes
• Symmetric calorons of higher charges and their large period limits

Cited by in corpus (10)

• A Smörgåsbord of Skyrmions
• Constrained instantons and kink-antikink collisions
• Nucleon-nucleon potential from instanton holonomies
• Finkelstein-Rubinstein constraints from ADHM data and rational maps
• Approximating the parallel transport of an induced connection
• Constrained instanton approximation of Skyrmions with massive pions
• Quantization of skyrmions using instantons
• JNR Skyrmions
• Instantons with continuous conformal symmetries: Hyperbolic and singular monopoles and more, oh my!
• Locations of JNR skyrmions