Skyrme chains are topologically-nontrivial solutions of the Skyrme model which are (quasi-)periodic in one spatial direction. We report numerical and analytic investigations which show that such solutions exist. Chains of 1-skyrmions are reasonably well approximated both as parallel vortex-antivortex pairs, and in terms of the holonomy of Yang-Mills calorons. As the period increases, the 1-skyrmions clump together, for example giving chains of 2-skyrmions or 4-skyrmions.
We investigate properties of self-gravitating isorotating Skyrmions in the generalized Einstein-Skyrme model with higher-derivative terms in the matter field sector. These stationary solutions are axially symmetric, regular and asymptotically flat. We provide a detailed account of the branch structure of the spinning solutions in the topological sector of degree one. We show that additional branches of solutions appear, as the angular frequency increases above some critical value, these "cloudy" configurations can be considered as a bound system of the spinning Skyrmions and "pion" excitations…
We study a Skyrme-like model with the Skyrme term and a sixth-order derivative term as higher-order terms, coupled to gravity and we construct Schwarzschild black hole Skyrme hair. We find, surprisingly, that the sixth-order derivative term alone cannot stabilize the black hole hair solutions; the Skyrme term with a large enough coefficient is a necessity.
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 $\mathcal{B} \leq 8$, with energies reproduced within 2% of the true minimisers. We also develop factorisation methods for studying clusters of instant…
A problem with the standard Skyrme model is that Skyrmion binding energies are around $15\%$, being much larger than the order $1\%$ binding energies of the nuclei that they aim to describe. Here we consider theories that extend the standard Skyrme model of pions by including rho mesons, via dimensional deconstruction of Yang-Mills theory with an extra dimension. We report the first results of parallel numerical computations of multi-Skyrmions in theories of this type, including a model that reduces Skyrmion energies below those of the standard Skyrme model whilst retaining exactly the same Fa…
Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology $π_3(S^3)$ and the monopole topology $π_2(S^2)$. With this we propose to classify the skyrmions by two topological numbers $(m,n)$, the monopole number $m$ and the shell (radial) number $n$. In this scheme the popular (non spherically symmetric) skyrmions are classified as the $(m,1)$ skyrmions but the spherically symmetric skyrmions are classified as the $(1,n)$ skyrmions, and the baryon number $B$ is given by $B=mn$. Mo…
A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound saturated for solutions of the pertinent Bogomolnyi equations supplemented by a so-called superpotential equation. In contrast to the gauged BPS baby Skyrme models considered previously, the superpotential equation is linear and, hence, completely solvable. Furthermore, the magnetic flux is quantized in units of $2π$, which allows, in principle, to define thi…
The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)-dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-…
Recently it has been pointed out that the skyrmions carry two independent topology, the baryon topology and the monopole topology. We provide more evidence to support this. In specific, we prove that the baryon number $B$ can be decomposed to the monopole number $m$ and the shell number $n$, so that $B$ is given by $B=mn$. This tells that the skyrmions may more conveniently be classified by two integers $(m,n)$. This is because the rational map which determines the baryon number in the popular multi-skyrmion solutions actually describes the monopole topology $π_2(S^2)$ which is different from …
We construct the first analytic examples of topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model within a finite box in (3+1)-dimensional flat space-time. There are two types of gauged solitons. The first type corresponds to gauged Skyrmions living within a finite volume. The second corresponds to gauged time-crystals (smooth solutions of the $U(1)$ gauged Skyrme model whose periodic time-dependence is protected by a winding number). The notion of electromagnetic duality can be extended for these two types of configurations in the sense that the electric and …
We consider a class of generalizations of the Skyrme model to five spacetime dimensions ($d=5$), which is defined in terms of an $O(5)$ sigma model. A special ansatz for the Skyrme field allows angular momentum to be present and equations of motion with a radial dependence only. Using it, we obtain: 1) everywhere regular solutions describing localised energy lumps (Skyrmions); 2) Self-gravitating, asymptotically flat, everywhere non-singular solitonic solutions (Skyrme stars), upon minimally coupling the model to Einstein's gravity; 3) both static and spinning black holes with Skyrme hair, the…
We derive a one-parameter family of gauged Skyrme models from Yang-Mills theory on $S^1\times\mathbb{R}^3$, in which skyrmions are well-approximated by calorons and monopoles. In particular we study the spherically symmetric solutions to the model with two distinct classes of boundary conditions, and compare them to calorons and monopoles. Calorons interpolate between instantons and monopoles in certain limits, and we observe similar behaviour in the constructed gauged Skyrme model in the weak and strong coupling limits. This comparison of calorons, monopoles, and skyrmions may be a way to fur…
We show that a suitable choice for the potential term in the two-dimensional baby Skyrme model yields solitons that have a short-range repulsion and a long-range attraction. The solitons are therefore aloof, in the sense that static multi-soliton bound states have constituents that preserve their individual identities and are sufficiently far apart that tail interactions yield small binding energies. The static multi-soliton solutions are found to have a cluster structure that is reproduced by a simple binary species particle model. In the standard three-dimensional Skyrme model of nuclei, sol…
We perform full two-dimensional (2D) numerical relaxations of isospinning soliton solutions in the baby Skyrme model in which the global $O(3)$ symmetry is broken by the 2D analogue of the pion mass term in the Skyrme model. In our calculations we explicitely allow the isospinning solitons to deform and to break the symmetries of the static configurations. We find that stable isospinning baby Skyrme solutions can be constructed numerically for all angular frequencies $ω\le \text{min}(μ,1)$, where $μ$ is the mass parameter of the model. Stable, rotationally-symmetric baby Skyrmion solutions for…
We study solutions of the Einstein-Skyrme model. Firstly we consider test field Skyrmions on the Kerr background. These configurations -- hereafter dubbed Skerrmions -- can be in equilibrium with a Kerr black hole (BH) by virtue of a synchronisation condition. We consider two sectors for Skerrmions. In the sector with non-zero baryon charge, Skerrmions are akin to the known Skyrme solutions on the Schwarzschild background. These `topological' configurations reduce to flat spacetime Skyrmions in a vanishing BH mass limit; moreoever, they never become "small" perturbations on the Kerr background…
We investigate the properties of spherically symmetric black hole solutions in the generalized Einstein-Skyrme model theory in four-dimensional asymptotically anti-de Sitter space-time. The dependencies of the Skyrmion fields on the cosmological constant and on the strength of the effective gravitational coupling are examined. We show that the increase of the absolute value of the cosmological constant qualitatively yields the same effect as increasing of the effective gravitational coupling. We confirm that, similar to the model in the asymptotically flat space-time, a necessary condition for…
We consider the baby Skyrme model in a physically motivated limit of reaching the restricted or BPS baby Skyrme model, which is a model that enjoys area-preserving diffeomorphism invariance. The perturbation consists of the kinetic Dirichlet term with a small coefficient $ε$ as well as the standard pion mass term, with coefficient $εm_1^2$. The pions remain lighter than the soliton for any $ε$ and therefore the model is physically acceptable, even in the $ε\to 0$ limit. The version of the BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform full numerical computations…
Exact analytic solutions of the Skyrme model defined on a spherically symmetric $R^{(1,1)} \times S^2$ geometry, chosen to mimic finite volume effects, are presented. The static and spherically symmetric configurations have non-trivial winding number and finite soliton mass. These configurations possess an extra topological charge, allowing for a novel BPS bound which can be saturated, unlike what happens in the standard case. Such solutions include exact multi-Skyrmions of arbitrary winding number, composed by interacting elementary Skyrmions. The values of the coupling constants and the comp…
We investigate how isospin affects the geometrical shape and energy of classical soliton solutions of topological charges $B=1-4,8$ in the Skyrme model. The novel approach in our work is that we study classically isospinning Skyrmions beyond the rigid-body approximation; that is, we explicitly allow the soliton solutions to deform and to break the symmetries of the static configurations. Our fully three-dimensional relaxation calculations reveal that the symmetries of isospinning Skyrme solitons can differ significantly from the ones of the static configurations. In particular, isospinning Sky…
We construct self-gravitating axially symmetric sphaleron solutions of the 3+1 dimensional Skyrme model coupled to Einstein gravity. The solutions are static and asymptotically flat, they are characterized by two integers n and m, where n is the winding numbers of the constituents and the second integer m defines type of the solution. These configuration correspond to the chains of charge n Skyrmions and charge -n anti-Skyrmions placed along the axis of symmetry in alternating order. We investigate the dependency of the masses of the gravitating sphalerons on the gravitational coupling. We fin…
