The vector BPS Skyrme model

Abstract

We analyze the vector meson formulation of the BPS Skyrme model in (3+1) dimensions, where the term of sixth power in first derivatives characteristic for the original, integrable BPS Skyrme model (the topological or baryon current squared) is replaced by a coupling between the vector meson ${\omega }_{\mu }$ and the baryon current. We find that the model remains integrable in the sense of generalized integrability and almost solvable (reducible to a set of two first order ODEs) for any value of the baryon charge. Further, we analyze the appearance of topological solitons for two one-parameter families of one vacuum potentials: the old Skyrme potentials and the so-called BPS potentials. Depending on the value of the parameters we find several qualitatively different possibilities. In the massless case we have a parameter region with no skyrmions, a unique compact skyrmion with a discontinuous first derivative at the boundary (equivalently, with a source term located at the boundary, which screens the topological charge), and Coulomb-like localized solitons. For the massive vector meson, besides the no-skyrmion region and a unique C-compact soliton, we find exponentially as well as power-like localized skyrmions. Further, we find (for a specific potential) BPS solutions, i.e., skyrmions saturating a Bogomolny bound (both for the massless and massive vector mesons) which are unstable for higher values of the baryon charge. The properties of the model are finally compared with its baby version in (2+1) dimensions, and with the original BPS Skyrme model, contributing to a better understanding of the latter.

Latex, 26 pages, 5 figures

References in corpus (15)

• Chiral Dynamics of Baryons from String Theory
• Dynamics of Baryons from String Theory and Vector Dominance
• Skyrmions, instantons and holography
• A BPS Skyrme model and baryons at large Nc
• Light Nuclei of Even Mass Number in the Skyrme Model
• Skyrmions with massive pions
• Nucleon Form Factors and Hidden Symmetry in Holographic QCD
• Integrable theories and loop spaces: fundamentals, applications and new developments
• Near-BPS Skyrmions: Non-shell configurations and Coulomb effects
• The gauged BPS baby Skyrme model
• Generalized self-dual Maxwell-Chern-Simons-Higgs model
• Multi-Skyrmions with Vector Mesons
• Baby Skyrmions stabilized by vector mesons
• Skyrme Model with Different Mass Terms
• The vector BPS baby Skyrme model

Cited by in corpus (10)

• Nuclear binding energies from a BPS Skyrme model
• Near BPS Skyrmions and Restricted Harmonic Maps
• Topological vortices in generalized Born-Infeld-Higgs electrodynamics
• Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario
• Compact Lumps
• Deformed self-dual magnetic monopoles
• Analytical BPS Maxwell-Higgs vortices
• Baby Skyrme models without a potential term
• Nontopological self-dual Maxwell-Higgs vortices
• Novel lumplike structures