Skyrmions, instantons and holography

Abstract

Some time ago, Atiyah and Manton observed that computing the holonomy of Yang-Mills instantons yields good approximations to static Skyrmion solutions of the Skyrme model. This paper provides an extension and explanation of this result, by proving that instanton holonomies produce exact solutions of a BPS Skyrme model, in which the Skyrme field is coupled to a tower of vector mesons. Neglecting any (or indeed all) of the vector mesons breaks the scale invariance and removes the BPS property of the Skyrmions. However, it is shown that a truncation of the BPS Skyrme theory, in which only the first vector meson is included, already moves the Skyrme model significantly closer to the BPS system. A theory that is close to a BPS system is required to reproduce the experimental data on binding energies of nuclei. A zero-mode quantization of the Skyrmion is performed in the truncated BPS theory and the results are compared to the physical properties of the nucleon. The approach is an analogue in five-dimensional Minkowski spacetime of a recent holographic construction of a Skyrme model by Sakai and Sugimoto, based on a string theory derivation of a Yang-Mills-Chern-Simons theory in a curved five-dimensional spacetime.

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Cited by in corpus (101)

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• Topological energy bounds for the Skyrme and Faddeev models with massive pions
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• BPS Skyrmions as neutron stars
• The Sakai-Sugimoto soliton
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• Solvable self-dual impurity models
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• Nuclei as near BPS-Skyrmions
• Neutron stars in the BPS Skyrme model: mean-field limit vs. full field theory
• Near-BPS Skyrmions: Non-shell configurations and Coulomb effects
• Nuclear binding energies from a BPS Skyrme model
• Loosening up the Skyrme model
• Topological energy bounds in generalized Skyrme models
• Skyrmions with vector mesons in the hidden local symmetry approach
• Hidden Local Symmetry and Infinite Tower of Vector Mesons for Baryons
• The gauged BPS baby Skyrme model
• Generalized Skyrme model with the loosely bound potential
• Geometric Models of Matter
• Topological solitons in the supersymmetric Skyrme model
• Skyrmions in models with pions and rho mesons
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• Aloof Baby Skyrmions
• Near-BPS Skyrmions: Constant baryon density
• Exact self-duality in a modified Skyrme model
• Analytic SU(N) Skyrmions at finite Baryon density
• Exploring the generalized loosely bound Skyrme model
• Scattering of Skyrmions
• Baryon chemical potential and in-medium properties of BPS skyrmions
• Realistic classical binding energies in the $\omega$-Skyrme model
• Skyrme-like models and supersymmetry in 3+1 dimensions
• Exact Self-Dual Skyrmions
• Super-exceptional embedding construction of the heterotic M5: Emergence of SU(2)-flavor sector
• Magnetothermodynamics of BPS baby skyrmions
• The Dielectric Skyrme model
• Skyrme crystals, nuclear matter and compact stars
• A Skyrme-like model with an exact BPS bound
• A Smörgåsbord of Skyrmions
• A model for gauged skyrmions with low binding energies
• Skyrmions and Hopfions in 3D Frustrated Magnets
• Rotational-vibrational coupling in the BPS Skyrme model of baryons
• Non-derivative Axionic Couplings to Nucleons at large and small N
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• Dielectric Skyrmions
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• A False Vacuum Skyrme Model for Nuclear Matter
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• Generalized skyrmion crystals with applications to neutron stars
• Flavor Symmetry and Topology Change in Nuclear Symmetry Energy for Compact Stars
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• Atiyah-Manton Construction of Skyrmions in Eight Dimensions
• A consistent two-skyrmion configuration space from instantons
• Background fields and self-dual Skyrmions
• Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential
• Solitons in the Gauged Skyrme-Maxwell Model
• Self-Duality in the Context of the Skyrme Model
• ADHM Polytopes
• Skyrmions from calorons
• Nucleon-nucleon potential from instanton holonomies
• The vector BPS baby Skyrme model
• Constrained instantons and kink-antikink collisions
• Skyrme model from 6d $\mathcal{N}$= (2,0) theory
• Rational Skyrmions
• Gravitating gauged BPS baby Skyrmions
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• A Quasi Self-Dual Skyrme Model
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• Holographic coordinates
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