A consistent two-skyrmion configuration space from instantons

To study a nuclear system in the Skyrme model one must first construct a space of low energy Skyrme configurations. However, there is no mathematical definition of this configuration space and there is not even consensus on its fundamental properties, such as its dimension. Here, we propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a vector meson which we identify with the ρ-meson. Each instanton generates a unique skyrmion and we reinterpret the 8N instanton moduli as physical degrees of freedom in the Skyrme model. In this picture a single skyrmion has six zero modes and two non-zero modes: one controls the overall scale of the solution and one the energy of the ρ-meson field. We study the N = 1 and N = 2 systems in detail. Two interacting skyrmions can excite the ρ through scattering, suggesting that the ρ and Skyrme fields are intrinsically linked. Our proposal is the first consistent manifold description of the two-skyrmion configuration space. The method can also be generalised to higher N and thus provides a general framework to study any skyrmion configuration space.

Analytic multi-Baryonic solutions in the SU(N)-Skyrme model at finite density

We construct explicit analytic solutions of the SU(N)-Skyrme model (for generic N) suitable to describe different phases of nuclear pasta at finite volume in (3 + 1) dimensions. The first type are crystals of Baryonic tubes (nuclear spaghetti) while the second type are smooth Baryonic layers (nuclear lasagna). Both, the ansatz for the spaghetti and the ansatz for the lasagna phases, reduce the complete set of Skyrme field equations to just one integrable equation for the profile within sectors of arbitrary high topological charge. We compute explicitly the total energy of both configurations in terms of the flavor number, the density and the Baryonic charge. Remarkably, our analytic results allow to compare explicitly the physical properties of nuclear spaghetti and lasagna phases. Our construction shows explicitly that, at lower densities, configurations with N = 2 light flavors are favored while, at higher densities, configurations with N = 3 are favored. Our construction also proves that in the high density regime (but still well within the range of validity of the Skyrme model) the lasagna configurations are favored while at low density the spaghetti configurations are favored. Moreover, the integrability property of the present configurations is not spoiled by the inclusion of the subleading corrections to the Skyrme model arising in the ’t Hooft expansion. Finally, we briefly discuss the large N limit of our configurations.

Magnetic particles and strings in iron langasite

Magnetic topological defects can store and carry information. Replacement of extended defects, such as domain walls and Skyrmion tubes, by compact magnetic particles that can propagate in all three spatial directions may open an extra dimension in the design of magnetic memory and data processing devices. We show that such objects can be found in iron langasite, which exhibits a hierarchy of non-collinear antiferromagnetic spin structures at very different length scales. We derive an effective model describing long-distance magnetic modulations in this chiral magnet and find unusual two- and three-dimensional topological defects. The order parameter space of our model is similar to that of superfluid 3He-A, and the particle-like magnetic defect is closely related to the Shankar monopole and hedgehog soliton in the Skyrme model of baryons. Mobile magnetic particles stabilized in non-collinear antiferromagnets can play an important role in antiferromagnetic spintronics.

Fractional Skyrmion molecules in a ℂPN−1 model

We study fractional Skyrmions in a ℂP2 baby Skyrme model with a generalization of the easy-plane potential. By numerical methods, we find stable, metastable, and unstable solutions taking the shapes of molecules. Various solutions possess discrete symmetries, and the origin of those symmetries are traced back to congruencies of the fields in homogeneous coordinates on ℂP2.

Gravitating Meron-like topological solitons in massive Yang–Mills theory and the Einstein–Skyrme model

We show that Merons in D-dimensional Einstein–Massive–Yang–Mills theory can be mapped to solutions of the Einstein–Skyrme model. The identification of the solutions relies on the fact that, when considering the Meron ansatz for the gauge connection $$A=\lambda U^{-1}dU$$ A = λ U - 1 d U , the massive Yang–Mills equations reduce to the Skyrme equations for the corresponding group element U. In the same way, the energy–momentum tensors of both theories can be identified and therefore lead to the same Einstein equations. Subsequently, we focus on the SU(2) case and show that introducing a mass for the Yang–Mills field restricts Merons to live on geometries given by the direct product of $$S^3$$ S 3 (or $$S^2$$ S 2 ) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for $$D=4$$ D = 4 and $$D=5$$ D = 5 . Finally, we comment on possible generalisations.

BPS Skyrme submodels of the five-dimensional Skyrme model

In this paper, we search for the BPS skyrmions in some BPS submodels of the generalized Skyrme model in five-dimensional spacetime using the BPS Lagrangian method. We focus on the static solutions of the Bogomolny’s equations and their corresponding energies with topological charge B > 0 is an integer. We consider two main cases based on the symmetry of the effective Lagrangian of the BPS submodels, i.e. the spherically symmetric and non-spherically symmetric cases. For the spherically symmetric case, we find two BPS submodels. The first BPS submodels consist of a potential term and a term proportional to the square of the topological current. The second BPS submodels consist of only the Skyrme term. The second BPS submodel has BPS skyrmions with the same topological charge B > 1, but with different energies, that we shall call “topological degenerate” BPS skyrmions. It also has the usual BPS skyrmions with equal energies, if the topological charge is a prime number. Another interesting feature of the BPS skyrmions, with B > 1, in this BPS submodel, is that these BPS skyrmions have non-zero pressures in the angular direction. For the non-spherically symmetric case, there is only one BPS submodel, which is similar to the first BPS submodel in the spherically symmetric case. We find that the BPS skyrmions depend on a constant k and for a particular value of k we obtain the BPS skyrmions of the first BPS submodel in the spherically symmetric case. The total static energy and the topological charge of these BPS skyrmions also depend on this constant. We also show that all the results found in this paper satisfy the full field equations of motions of the corresponding BPS submodels.

Near-BPS baby Skyrmions with Gaussian tails

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 $$ \upepsilon {m}_1^2 $$ ϵ m 1 2 . The pions remain lighter than the soliton for any ϵ and therefore the model is physically acceptable, even in the ϵ → 0 limit. The version of the BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform full numerical computations in the ϵ → 0 limit and even reach the strict ϵ = 0 case, finding new nontrivial BPS solutions, for which we do not yet know the analytic form.