Gauged Hopfions

Abstract

We discuss the $U(1)$ gauged version of the 3+1 dimensional Faddeev-Skyrme model supplemented by the Maxwell term. We show that there exist axially symmetric static solutions coupled to the non-integer toroidal flux of magnetic field, which revert to the usual Hopfions ${\mathcal{A}}_{m,n}$ of lower degrees $Q=mn$ in the limit of the gauge coupling constant vanishing. The masses of the static gauged Hopfions are found to be less than the corresponding masses of the usual ungauged solitons ${\mathcal{A}}_{1,1}$ and ${\mathcal{A}}_{2,1}$ respectively, they become lighter as gauge coupling increases. The dependence of the solutions on the gauge coupling is investigated. We find that in the strong coupling regime the gauged Hopfion carries two magnetic fluxes, which are quantized in units of $2\pi$, carrying $n$ and $m$ quanta respectively. The first flux encircles the position curve and the second one is directed along the symmetry axis. Effective quantization of the field in the gauge sector may allow us to reconsider the usual arguments concerning the lower topological bound in the Faddeev-Skyrme-Maxwell model.

10 pages, 5 figures

References in corpus (34)

• Knots and Particles
• Partially Dual variables in SU(2) Yang-Mills Theory
• To be or knot to be?
• Hidden symmetry and knot solitons in a charged two-condensate Bose system
• Stationary ring solitons in field theory - knots and vortons
• Multisolitons in a Two-dimensional Skyrme Model
• Static solitons with non-zero Hopf number
• A Skyrme-type proposal for baryonic matter
• Bogomol'nyi solitons in a gauged $O(3)$ sigma model
• Knots in a Spinor Bose-Einstein Condensate
• Hopf Solitons on S^3 and R^3
• The baby Skyrme models and their multi-skyrmions
• Knots in the Skyrme-Faddeev model
• Skyrmions in a truncated BPS theory
• Monopole-Antimonopole Chains and Vortex Rings
• Monopole--Antimonopole Chains
• Monopoles, Antimonopoles and Vortex Rings
• Skyrme-Maxwell Solitons in (2+1) Dimensions
• Static solutions in the U(1) gauged Skyrme model
• Torus knots as Hopfions
• Non-Meissner electrodynamics and knotted solitons in two-component superconductors
• Spinning U(1) gauged Skyrmions
• SO(3) Gauged Soliton of an O(4) Sigma Model on $R_3$
• The gauged BPS baby Skyrme model
• Isospinning baby Skyrmion solutions
• Massive Hopfions
• Isospinning hopfions
• Classically Isospinning Hopf Solitons
• Isorotating Baby Skyrmions
• Skyrmion--Anti-Skyrmion Chains
• Electromagnetic Interaction in the System of Multimonopoles and Vortex Rings
• Energy Bounds of Linked Vortex States
• Supercurrent coupling destabilizes knot solitons
• Hopfion canonical quantization

Cited by in corpus (4)

• Gauged Aloof Baby Skyrme Model
• Solitons in the Gauged Skyrme-Maxwell Model
• Gauged merons
• Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model