Rational Maps, Monopoles and Skyrmions

Abstract

We discuss the similarities between BPS monopoles and Skyrmions, and point to an underlying connection in terms of rational maps between Riemann spheres. This involves the introduction of a new ansatz for Skyrme fields. We use this to construct good approximations to several known Skyrmions, including all the minimal energy configurations up to baryon number nine, and some new solutions such as a baryon number seventeen Skyrme field with the truncated icosahedron structure of a buckyball. The new approach is also used to understand the low-lying vibrational modes of Skyrmions, which are required for quantization. Along the way we discover an interesting Morse function on the space of rational maps which may be of use in understanding the Sen forms on the monopole moduli spaces.

35pp including four figures, typos corrected, appearing in Nuclear Physics B

References in corpus (3)

• Symmetric Skyrmions
• Normal Mode Spectrum of the Deuteron in the Skyrme Model
• Normal Modes of the B=4 Skyrme Soliton

Cited by in corpus (248)

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• Skyrmions and the alpha-particle model of nuclei
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• Skyrmions in models with pions and rho mesons
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• Black hole and BTZ-black string in the Einstein-SU(2) Skyrme model
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• The Inhomogeneous Phase of Dense Skyrmion Matter
• Scaling Identities for Solitons beyond Derrick's Theorem
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• A Monopole Wall
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• Monopole Planets and Galaxies
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• A generating function for all-orders skyrmions
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• Skyrmion--Anti-Skyrmion Chains
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• Finkelstein-Rubinstein constraints for the Skyrme model with pion masses
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• Quantization of T_d- and O_h-symmetric Skyrmions
• Interactions of B = 4 Skyrmions
• Classical Skyrmions -- Static Solutions and Dynamics
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• Platonic Sphalerons
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• Platonic Sphalerons in the Presence of a Dilaton Field
• Automorphic Lie Algebras with dihedral symmetry
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• Folding in the Skyrme Model
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• The BPS sectors of the Skyrme model and their non-BPS extensions
• The quantization of the B=1 and B=2 Skyrmions
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• Complex BPS Skyrmions with real energy
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• Monopoles and Harmonic Maps
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• Baby Skyrmions on the Two-Sphere
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• Restricting profile function of hedgehog Skyrmion
• Atiyah-Manton Construction of Skyrmions in Eight Dimensions
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• Hopf instantons and the Liouville equation in target space
• Excited Platonic Sphalerons in the Presence of a Dilaton Field
• Hopfions interaction from the viewpoint of the product ansatz
• Linking number of vortices as baryon number
• The bubbles of matter from multiskyrmions
• Flavored exotic multibaryons and hypernuclei in topological soliton models
• eta-^4He Bound States in the Skyrme Model
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• An Improved Harmonic Map Ansatz
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• Multibaryons as Symmetric Multiskyrmions
• Self-Duality in the Context of the Skyrme Model
• Rotating One-Half Topological Charge Dyon
• ADHM Polytopes
• Multibaryons in the collective coordinate approach to the SU(3) Skyrme model
• Skyrme Model with Different Mass Terms
• Skyrmions from calorons
• The effect of pion mass on Skyrme configurations
• Particle-like platonic solutions in scalar gravity
• Jacobi Elliptic Monopole-Antimonopole Pair Solutions
• Hypernuclei as chiral solitons
• Semiclassical Quantization of Hopf Solitons
• New Topological Structures of Skyrme Theory: Baryon Number and Monopole Number
• Review of Rotational Symmetry Breaking in Baby Skyrme Models
• Hopf Solitons from Instanton Holonomy
• Black holes with Skyrmion-anti-Skyrmion hairs
• Finkelstein-Rubinstein constraints from ADHM data and rational maps
• Rational Skyrmions
• Vacuum Decay Induced by False Skyrmions
• Gravitating SU(N) Monopoles from Harmonic maps
• Soliton stability in some knot soliton models
• Approximate analytical solutions of the baby Skyrme model
• Anomaly-induced charges in baryons
• Backreacted Coulomb energy in the Skyrme model
• Electrically Charged One and a Half Monopole Solution
• Gravitating Dyons with Large Electric Charge
• Discrete Skyrmions in 2+1 and 3+1 Dimensions
• The $\alpha$ particle as a canonically quantized multiskyrmion
• Nuclear bound states of antikaons, or quantized multiskyrmions?
• Symmetric calorons of higher charges and their large period limits
• The Deuteron as a Canonically Quantized Biskyrmion
• Skyrmions, Rational Maps & Scaling Identities
• Collective coordinates of the Skyrme model coupled with fermions
• Monopoles from Rational Maps
• False vacuum Skyrmions revisited
• Knots in Physics
• Degeneracy of the quarks, shell structure in the chiral soliton
• The nucleus as a fluid of skyrmions: Energy levels and nucleon properties in the medium
• Hereditary Automorphic Lie Algebras
• Remarks on the existence of Spinning Membrane Actions
• Nonlinear rigid-body quantization of Skyrmions
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• Angularly localized Skyrmions
• SU(5) Gravitating Monopoles
• Bogomolny equations for the BPS Skyrme models with impurity
• Selected problems of baryons spectroscopy: chiral soliton versus quark models
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• A multishell solution in the Skyrme model
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• Holographic coordinates
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• Generalized Half-Dyon in SU(2) Yang-Mills-Higgs Theory
• A Skyrme Model with Novel Chiral Symmetry Breaking
• BPS deformations of the Skyrme model
• The Spinning Membrane and Skyrmions Revisited
• Isospinning Skyrmions
• Chiral Dirac-Born-Infeld solitons with SDiff symmetry
• Lattice Three-Dimensional Skyrmions Revisited
• Experimental and Theoretical Evidence for Extended Particle Models
• Neutron Rich Hypernuclei in Chiral Soliton Model
• Construction of Hopfion Crystals
• JNR Skyrmions
• Locations of JNR skyrmions
• Platonic solutions of the discrete Nahm equation
• Modes of the Sakai-Sugimoto soliton
• Interaction of hopfions of charge 1 and 2 from product ansatz
• Dyons of One Half Monopole Charge
• Noncanonicaly Embedded Rational Map Soliton in Quantum SU(3) Skyrme Model
• Equivariant functions and rational differential operators
• Discrete BPS Skyrmions
• Rescaling of quantized skyrmions: from nucleon to baryons with heavy flavor
• Moduli Spaces of Lumps on Real Projective Space
• Recent Developments in the Skyrme Model
• Elastic energy of liquid crystals in convex polyhedra