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A discussion of the stability of self-gravitating Skyrmions, with a large winding number N, in a Schwarzschild type of metric, is presented for the case where an isospin chemical potential is introduced. It turns out that the chemical potential stabilizes the behavior of the Skyrmion discussed previously in the literature. This analysis is carried on in the framework of a variational approach using different ansatze for the radial profile of the Skyrmion. We found a divergent behavior for the size of the Skyrmion, associated to a certain critical value μ_c of the chemical potential. At this point, the mass of the Skyrmion vanishes. μ_c is essentially independent of gravitating effects. The stability of a large N skyrmion against decays into single particles is also discussed.

Currently the quantitative description of confinement inside nuclear matter is exclusively limited to computer experiments, mainly on lattices, and concentrating upon calculating the static potential. There is no independent reference for comparison and support of the results, especially when it comes to the quark potential in the continuum limit. Yet, we are entitled to be optimistic, for the basic results of these calculations seem to be correct from an entirely different point of view, suggested by Manton's geometrization of Skyrme theory. The present work shows the reasons of this point of view, and offers a static potential that might serve as independent reference for comparison and endorsement of any lattice calculations, and in fact of any structural hypotheses of nuclear matter. A historical review of the pertinent key moments in the history of modeling of nuclear matter, as well as an outlook anticipating the necessary future work, close the argument.

In this paper, we will describe recent advances in analytical methods to construct exact solutions of the Skyrme model (and its generalizations) representing inhomogeneous Hadronic condensates living at finite Baryon density. Such novel analytical tools are based on the idea to generalize the well-known spherical hedgehog ansatz to situations (relevant for the analysis of finite density effects) in which there is no spherical symmetry anymore. Besides the intrinsic mathematical interest to find exact solutions with nonvanishing Baryonic charge confined to a finite volume, this framework opens the possibility to compute important physical quantities which would be difficult to compute otherwise.

Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein–Rubinstein theory for Skyrmions/kinks to topological defects, and using non-Abelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix-valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to $\frac{\hslash }{2}$, i.e. proton spin decomposition has no meaning in this approach.

We address a simple model allowing the existence of domain walls with orientational moduli localized on them. Within this model, we discuss an analytic solution and explore it in the context of previously known results. We discuss the existence of one-dimensional domain walls localized on two-dimensional ones, and construct the corresponding effective action. In the low-energy limit, which is the $𝕆(3)$ sigma-model, we discuss the existence of skyrmions localized on domain walls, and provide a solution for a skyrmion configuration, based on an analogy with instantons. We perform symmetry analysis of the initial model and of the low-energy theory on the domain wall worldvolume.

A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a θ-term determines the spin and statistics of these skyrmions.

We find approximate solutions for the two-dimensional nonlinear $\mathrm{\Sigma }$-model with Dzyalioshinkii–Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

Skyrmions are topological solitons that emerge in many physical contexts. In magnetism, they appear as textures of the spin-density field stabilized by different competing interactions and characterized by a topological charge that counts the number of times the order parameter wraps the sphere. They behave as classical objects when the spin texture varies slowly on the scale of the microscopic lattice of the magnet. However, the fast development of experimental tools to create and stabilize skyrmions in thin magnetic films has led to a rich variety of textures, sometimes of atomistic sizes. In this paper, we discuss, in a pedagogical manner, how to introduce quantum interference in the translational dynamics of skyrmion textures, starting from the micromagnetic equations of motion for a classical soliton. We study how the nontrivial topology of the spin texture manifests in the semiclassical regime, when the microscopic lattice potential is treated quantum-mechanically, but the external driving forces are taken as smooth classical perturbations. We highlight close relations to the fields of noncommutative quantum mechanics, Chern–Simons theories, and the quantum Hall effect.

Skyrmions are topological solitons that describe baryons within a nonlinear theory of pions. In holographic QCD, baryons correspond to topological solitons in a bulk theory with an extra spatial dimension. Thus, the three-dimensional Skyrmion lifts to a four-dimensional holographic Skyrmion in the bulk. We begin this review with a description of the simplest example of this correspondence, where the holographic Skyrmion is exactly the self-dual Yang–Mills instanton in flat space. This places an old result of Atiyah and Manton within a holographic framework and reveals that the associated Skyrme model extends the nonlinear pion theory to include an infinite tower of vector mesons, with specific couplings for a BPS theory. We then describe the more complicated curved space version that arises from the string theory construction of Sakai and Sugimoto. The basic concepts remain the same but the technical difficulty increases as the holographic Skyrmion is a curved space version of the Yang–Mills instanton, so self-duality and integrability are lost. Finally, we turn to a low-dimensional analog of holographic Skyrmions, where aspects such as multi-baryons and finite baryon density are amenable to both numerical computation and an approximate analytic treatment.

The classical treatment of the Kepler problem leaves room for the description of the space region of the central body by a hyperbolic geometry. If the correspondence between the empty space and the space filled with matter is taken to be a harmonic mapping, then the region of atomic nucleus, like the one of the Sun for the planetary system proper, is described by hyperbolic skyrmions. This fact makes possible the description of the nuclear matter within framework of general relativity. The classical “hedgehog” solution for skyrmions can then be classically interpreted in terms of the characterizations of intra-nuclear forces.

We propose a new approach of many-particle quantum hydrodynamics to describe a system of interacting magnetic skyrmions in the external fields. The model is based on the description of skyrmions as a fluid of point-like particles. The equations of many-particle quantum hydrodynamics are obtained for a system of skyrmions with induced dipole moments and charges. The dipole–dipole interaction between dipoles and the Coulomb interaction between charges are taken into account. The influence of quantum effects in the form of the Bohm quantum potential is obtained. The contribution of Magnus effect to the dynamics of dipoles current density is predicted. The electron–skyrmion interactions are considered, based on a two-fluid model of quantum hydrodynamics with separate description of spin-up and spin-down electrons on the background of skyrmion lattice. The proposed model can be further used to study the dynamical effects in a system of skyrmions in the external fields.

A self-gravitating Skyrmion is an analytic and globally regular solution of the Einstein–Skyrme system with nonvanishing topological charge. The spacetime is the direct product $R\times S^3$ and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX and, through an analytic continuation, it can also be turned into a transversable asymptotically AdS Lorentzian wormhole. The stress–energy of this wormhole satisfies physically realistic energy conditions and the only “exotic matter” required by it is a negative cosmological constant.

About two decades ago, Gerry Brown pushed me to study hadron physics using hadronic models based on the hidden local symmetry (HLS). Since then, I have been involving many works related to the HLS. In this contribution to Gerry’s memorial, I will summarize my recent analyses associated with the HLS. After a very brief summary of the HLS, I will show a way to determine parameters of the HLS model from holographic QCD models. This model provides a soliton solution which is identified with the nucleon. I will briefly introduce a model in which the solitons are put onto a crystal lattice for simulating nuclear matter. The results suggest existence of the chiral invariant mass of nucleon. I also briefly review my recent analyses on the nuclear matter by using a hadronic model including nucleon field together with the $\pi$, $\sigma$, $\rho$ and $\omega$ mesons based on the parity doublet structure of nucleon combined with the HLS, in which the chiral invariant mass of the nucleon is naturally embedded. The result implies that studying effective masses of nucleons will give a clue for the chiral invariant mass. Finally, I will show our recent analysis on the medium modification of charmed meson masses using a chiral model based on the chiral doubling structure of charmed mesons. The result shows that the masses of the chiral partners of charmed mesons become closer in high density reflecting the particle chiral symmetry restoration in medium.

In this talk, we report a recent investigation on the energy-momentum tensor form factors of the nucleon in nuclear medium, based on the framework of the in-medium modified chiral soliton model. The model was constructed by taking into account the influence of the surrounding environment to the mesonic sector (π-, ρ- and ω-meson properties). We briefly discuss the results of the energy-momentum tensor form factors.

Intriguing electromagnetic phenomena can show up in a solid when the electrons spins take a helical form. To name a few, the cycloidal order of the spin moments can produce the electric polarization and generate the multiferroics where the ferroelectric and magnetic orders coexist and enable the cross control of the magnetism with electric field. When spin helices hybridize to form with plural propagation directions, the topological spin textures such as magnetic skyrmion lattice emerge, hosting the large emergent magnetic field or Berry curvature acting on the conduction electrons. Furthermore, the dynamics of these helical spin forms, as excited by electric current flow, can generate the emergent electric field acting on the electrons and hence cause a sort of electromagnetic induction. Such emergent electromagnetic induction based on the spin chiral matter is applied to the design of nanometric inductor element.

About two decades ago, Gerry Brown pushed me to study hadron physics using hadronic models based on the hidden local symmetry (HLS). Since then, I have been involving many works related to the HLS. In this contribution to Gerry’s memorial, I will summarize my recent analyses associated with the HLS. After a very brief summary of the HLS, I will show a way to determine parameters of the HLS model from holographic QCD models. This model provides a soliton solution which is identified with the nucleon. I will briefly introduce a model in which the solitons are put onto a crystal lattice for simulating nuclear matter. The results suggest existence of the chiral invariant mass of nucleon. I also briefly review my recent analyses on the nuclear matter by using a hadronic model including nucleon field together with the π, σ, ρ and ω mesons based on the parity doublet structure of nucleon combined with the HLS, in which the chiral invariant mass of the nucleon is naturally embedded. The result implies that studying effective masses of nucleons will give a clue for the chiral invariant mass. Finally, I will show our recent analysis on the medium modification of charmed meson masses using a chiral model based on the chiral doubling structure of charmed mesons. The result shows that the masses of the chiral partners of charmed mesons become closer in high density reflecting the particle chiral symmetry restoration in medium.

Kantowski-Sachs cosmological models sourced by a Skyrme field and a cosmological constant are considered in the framework of General Relativity. A qualitative analysis of the equations and some physically interesting features of the model are reviewed.

We study baryons and baryonic matter in holographic QCD with multi-D brane system in type IIA superstring theory. Baryons are described as "Skyrmions" of a four-dimensional meson effective action which is derived from the five-dimensional Yang-Mills theory formulated in holographic QCD. We compare our results with those in the hidden local symmetry approach on the flat space-time, and show that the curved extra-dimension largely changes the roles of (axial) vector mesons for the baryons.

In general, effective low-energy Lagrangian models of composite electroweak symmetry breaking (EWSB) have soliton solutions that may be identified with technibaryons. The masses of such states may be related to the coefficients of fourth-order terms in the effective Lagrangian, as in QCD. We show how the current theoretical and phenomenological constraints on the corresponding fourth-order coefficients in the electroweak theory could be used to estimate qualitative lower and upper bounds on the lightest electroweak baryon mass. We point out that in strongly-interacting models of electroweak symmetry breaking, non-Skyrmion-like solitons are also possible. Future data from the LHC as well as dark matter experiments will constrain this possibility. With the currently available data the upper bound on the mass of the electroweak soliton is between 18 and 59 TeV. With improved information that LHC is likely to provide on quartic terms in the electroweak Lagrangian, these bounds might be reduced to 4.6 to 8.1 TeV.