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The Skyrme model and its generalisations provide a conceptually appealing field-theory basis for the description of nuclear matter and, after its coupling to gravity, also of neutron stars. In particular, a specific Skyrme submodel, the so-called Bogomol'nyi-Prasad-Sommerfield (BPS) Skyrme model, allows both for an exact field-theoretic and a mean-field treatment of neutron stars, as a consequence of its perfect fluid property. A pure BPS Skyrme model description of neutron stars, however, only describes the neutron star core, by construction. Here we consider different possibilities to extrapolate a BPS Skyrme neutron star at high baryon density to a description valid at lower densities. In the exact field-theoretic case, a simple effective description of the neutron star crust can be used, because the exact BPS Skyrme neutron star solutions formally extend to sufficiently low densities. In the mean-field case, on the other hand, the BPS Skyrme neutron star solutions always remain above the nuclear saturation density and, therefore, must be joined to a different nuclear physics equation of state already for the outer core. We study the resulting neutron stars in both cases, facilitating an even more complete comparison between Skyrmionic neutron stars and neutron stars obtained from other approaches, as well as with observations., Comment: Latex, 21 pages, 3 figures; v3: version as accepted in PRD

In the Skyrme model of nucleons and nuclei, the spin excitation energy of the nucleon is traditionally calculated by a fit of the rigid rotor quantization of spin/isospin of the fundamental Skyrmion (the hedgehog) to the masses of the nucleon and the Delta resonance. The resulting, quite large spin excitation energy of the nucleon of about $ 73\, \mbox{MeV}$ is, however, rather difficult to reconcile with the small binding energies of physical nuclei, among other problems. Here we argue that a more reliable value for the spin excitation energy of the nucleon, compatible with many physical constraints, is about $ 16\, \mbox{MeV}$. The fit of the rigid rotor to the Delta, on the other hand, is problematic in any case, because it implies the use of a nonrelativistic method for a highly relativistic system., Comment: Latex, 8 pages, no figures

In this review, we summarise the main features of the BPS Skyrme model which provides a physically well-motivated idealisation of atomic nuclei and nuclear matter: 1) it leads to zero binding energies for classical solitons (while realistic binding energies emerge owing to the semiclassical corrections, the Coulomb interaction and isospin breaking); 2) it describes a perfect non-barotropic fluid already at the microscopic (field theoretical) level which allows to study thermodynamics beyond the mean-field limit. These properties allow for an approximate but analytical calculation of binding energies of the most abundant nuclei, for a determination of the equation of state of skyrmionic matter (both in the full field theory and in a mean-field approximation) as well as the description of neutron stars as Skyrme solitons with a very good agreement with available observational data. All these results suggest that the proper low energy effective model of QCD should be close to the BPS Skyrme model in a certain sense (a "near-BPS Skyrme model"), with a prominent role played by the BPS part., Comment: 40 pages, Latex, 10 figures. Contribution to: M. Rho, I. Zahed, Eds., The Multifaceted Skyrmion, 2nd Edition, World Scientific, Singapore

We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particular, we analytically compute the baryon chemical potential both in the full field theory and in a mean-field approximation. In the full field theory case, we find that the baryon chemical potential is always exactly proportional to the baryon density, for arbitrary solutions. We further find that, in the mean-field approximation, the BPS Skyrme model approaches the Walecka model in the limit of high density - their thermodynamical functions as well as the equation of state agree in this limit. This fact allows to read off some properties of the $\omega$-meson from the BPS Skyrme action, even though the latter model is entirely based on the (pionic) $SU(2)$ Skyrme field. On the other hand, at low densities, at the order of the usual nuclear matter density, the equations of state of the two models are no longer universal, such that a comparison depends on some model details. Still, also the BPS Skyrme model gives rise to nuclear saturation in this regime, leading, in fact, to an exact balance between repulsive and attractive forces. The perfect fluid aspects of the BPS Skyrme model, which, together with its BPS properties, form the base of our results, are shown to be in close formal analogy with the Eulerian formulation of relativistic fluid dynamics. Within this analogy, the BPS Skyrme model, in general, corresponds to a non-barotropic perfect fluid., Comment: Latex, 28 pages, 3 figures

Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtained in the full field theory, where gravitational back reaction is completely taken into account, with calculations in a mean-field approximation using the Tolman-Oppenheimer-Volkoff approach. In the latter case, a mean-field-theory equation of state is derived from the original BPS field theory. We show that in the full field theory, where the energy density is non-constant even at equilibrium, there is no universal and coordinate independent equation of state of nuclear matter, in contrast to the mean-field approximation. We also study how neutron star properties are modified by going beyond mean field theory, and find that the differences between mean field theory and exact results can be considerable. Further, we compare both exact and mean-field results with some theoretical and phenomenological constraints on neutron star properties, demonstrating thus the relevance of our model even in its most simple version., Comment: Latex file, 37 pages, 12 figures; v2: discussions improved, comparison to other neutron star models and results added; as accepted for publication in Phys. Rev. C

We present a concrete model of a low energy effective field theory of QCD, the well-known Skyrme Model. Specifically, we will work with the BPS submodel in order to describe the binding energies of nuclei. This BPS Skyrme model is characterized by having a saturated bound for the energy proportional to the baryon number of the nuclei. After presenting this classical result, we will proceed with a semi-classical quantization of the coordinates of spin and isospin. Then, with the further inclusion of the Coulomb interaction as well as a small explicit breaking of the isospin symmetry, we finally calculate the binding energies of nuclei, where an excellent agreement has been found for the nuclei with high baryon number. Besides this, we also apply this model to the study of some thermodynamic properties and to neutron stars., Comment: 7 pages, 4 figures; Proceedings for the 37th International Conference on High Energy Physics (ICHEP), Valencia 2014

The BPS Skyrme model has been demonstrated already to provide a physically intriguing and quantitatively reliable description of nuclear matter. Indeed, the model has both the symmetries and the energy-momentum tensor of a perfect fluid, and thus represents a field theoretic realization of the "liquid droplet" model of nuclear matter. In addition, the classical soliton solutions together with some obvious corrections (spin-isospin quantization, Coulomb energy, proton-neutron mass difference) provide an accurate modeling of nuclear binding energies for heavier nuclei. These results lead to the rather natural proposal to try to describe also neutron stars by the BPS Skyrme model coupled to gravity. We find that the resulting self-gravitating BPS Skyrmions provide excellent results as well as some new perspectives for the description of bulk properties of neutron stars when the parameter values of the model are extracted from nuclear physics. Specifically, the maximum possible mass of a neutron star before black-hole formation sets in is a few solar masses, the precise value depending on the precise values of the model parameters, and the resulting neutron star radius is of the order of 10 km., Comment: 15 pages, 4 figures, Latex, 2 figures added, discussion extended and improved, references added; published version

One problem in the application of the Skyrme model to nuclear physics is that it predicts too large a value for the compression modulus of nuclear matter. Here we investigate the thermodynamics of the BPS Skyrme model at zero temperature and calculate its equation of state. Among other results, we find that classically (i.e. without taking into account quantum corrections) the compressibility of BPS skyrmions is, in fact, infinite, corresponding to a zero compression modulus. This suggests that the inclusion of the BPS submodel into the Skyrme model lagrangian may significantly reduce this too large value, providing further evidence for the claim that the BPS Skyrme model may play an important role in the description of nuclei and nuclear matter., Comment: Latex, 26 pages, 1 figure; v2: some typos corrected, version accepted for publication in Phys. Rev. D

We use the classical BPS soliton solutions of the BPS Skyrme model together with corrections from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a small explicit breaking of the isospin symmetry - accounting for the proton-neutron mass difference - to calculate nuclear binding energies. We find that the resulting binding energies are already in excellent agreement with their physical values for heavier nuclei, demonstrating thereby that the BPS Skyrme model is a distinguished starting point for a detailed quantitative investigation of nuclear and low-energy strong interaction physics., Comment: 10 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1309.0820

Recently, within the space of generalized Skyrme models, a BPS submodel was identified which reproduces some bulk properties of nuclear matter already on a classical level and, as such, constitutes a promising field theory candidate for the detailed and reliable description of nuclei and hadrons. Here we extend and further develop these investigations by applying the model to the calculation of nuclear binding energies. Concretely, we calculate these binding energies by including the classical soliton energies, the excitation energies from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies and a small explicit isospin symmetry breaking, which accounts for the mass difference between proton and neutron. The integrability properties of the BPS Skyrme model allow, in fact, for an analytical calculation of all contributions, which may then be compared with the semi-empirical mass formula. We find that for heavier nuclei, where the model is expected to be more accurate on theoretical grounds, the resulting binding energies are already in excellent agreement with their physical values. This result provides further strong evidence for the viability of the BPS Skyrme model as a distinguished starting point and lowest order approximation for the detailed quantitative investigation of nuclear and hadron physics., Comment: Latex, 25 pages, 3 figures

We calculate the rotational-vibrational spectrum in the BPS Skyrme model for the hedgehog skyrmion with baryon number one. The resulting excitation energies for the nucleon and delta Roper resonances are slightly above their experimental values. Together with the fact that in the standard Skyrme model these excitation energies are significantly lower than the experimental ones, this provides strong evidence for the conjecture that the inclusion of the BPS Skyrme model is necessary for a successful quantitative description of physical properties of baryons and nuclei., Comment: Latex, 9 pages. v2: some references added

Within the class of field theories with the field contents of the Skyrme model, one submodel can be found which consists of the square of the baryon current and a potential term only. For this submodel, a Bogomolny bound exists and the static soliton solutions saturate this bound. Further, already on the classical level, this BPS Skyrme model reproduces some features of the liquid drop model of nuclei. Here, we investigate the model in more detail and, besides, we perform the rigid rotor quantization of the simplest Skyrmion (the nucleon). In addition, we discuss indications that the viability of the model as a low energy effective field theory for QCD is further improved in the limit of a large number of colors N_c., Comment: latex, 23 pages, 1 figure, a numerical error in section 3.2 corrected; matches published version

The Skyrme model is a low-energy effective field theory for QCD, where the baryons emerge as soliton solutions. It is, however, not so easy within the standard Skyrme model to reproduce the almost exact linear growth of the nuclear masses with the baryon number (topological charge), due to the lack of Bogomolny solutions in this model, which has also hindered analytical progress. Here we identify a submodel within the Skyrme-type low energy effective action which does have a Bogomolny bound and exact Bogomolny solutions, and therefore, at least at the classical level, reproduces the nuclear masses by construction. Due to its high symmetry, this model qualitatively reproduces the main features of the liquid droplet model of nuclei. Finally, we discuss under which circumstances the proposed sextic term, which is of an essentially geometric and topological nature, can be expected to give a reasonable description of properties of nuclei., Comment: 11 pages, 2 figures, latex. v3: Extended and revised version, some clarifications added. Some references and 2 figures added. v4: matches published version