BPS Skyrme Model Research Articles

Rotational-vibrational coupling in the BPS Skyrme model of baryons

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 required for a successful quantitative description of physical properties of baryons and nuclei.

Symmetries and exact solutions of the BPS Skyrme model

The BPS Skyrme model is a specific subclass of Skyrme-type field theories which possesses both a BPS bound and infinitely many soliton solutions (skyrmions) saturating that bound. A related property, the existence of a large group of symmetry transformations, allows for solutions of rather general shapes, which is in contrast to the situation for the original Skyrme model, where soliton solutions usually have some fixed shapes. We study here the classical symmetries of the BPS Skyrme model, applying them to construct soliton solutions with some prescribed shapes, which constitutes a further step to understand the similarities and differences with the original Skyrme model.

Skyrmions in a truncated BPS theory

Recently, it has been shown that (4 + 1)-dimensional Yang-Mills theory may be written as a (3 + 1)-dimensional BPS Skyrme model, in which the Skyrme field is coupled toan infinite tower of vector mesons. Truncating this tower to a single vector meson yields an extension of the standard Skyrme model to a theory of pions coupled to the ρ meson, with the significant simplification that no additional free parameters are introduced. The present paper is concerned with this truncated theory and results are presented for Skyrmions with baryon numbers one to four. The approach involves the use of an extended version of the Atiyah-Manton construction, in which the Skyrme field is approximated by the holonomy of a Yang-Mills instanton. It is found that the coupling to the ρ meson significantly reduces Skyrmion binding energies, to produce an improved comparison with the experimental data on nuclei. A truncation that includes both a vector and an axial vector meson is also investigated, providing a model of pions, the ρ meson and the a 1 meson. Binding energies are further reduced by the inclusion of this additional meson, shifting the Skyrmion energies a little closer to those of nuclei. Fixing the energy unit by equating the energy of the baryon number four Skyrmion to the He4 mass, yields masses for all lower baryon numbers that are within 20MeV of the experimental values, which is an error that is four times smaller than in the standard Skyrme model.

A BPS Skyrme model

Within the set of generalized Skyrme models, we identify a submodel which has both infinitely many symmetries and a Bogomolny bound which is saturated by infinitely many exact soliton solutions. Concretely, the submodel consists of the square of the baryon current and a potential term only. Further, already on the classical level, this BPS Skyrme model reproduces some features of the liquid drop model of nuclei. Here, we review the properties of the model and we discuss the semiclassical quantization of the simplest Skyrmion (the nucleon).

BPS Skyrme model and baryons at largeNc

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.

Skyrmions, instantons and holography

Some time ago, Atiyah and Manton observed that computing the holonomy of Yang-Mills instantons yields good approximations to static Skyrmion solutions of the Skyrme model. This paper provides an extension and explanation of this result, by proving that instanton holonomies produce exact solutions of a BPS Skyrme model, in which the Skyrme field is coupled to a tower of vector mesons. Neglecting any (or indeed all) of the vector mesons breaks the scale invariance and removes the BPS property of the Skyrmions. However, it is shown that a truncation of the BPS Skyrme theory, in which only the first vector meson is included, already moves the Skyrme model significantly closer to the BPS system. A theory that is close to a BPS system is required to reproduce the experimental data on binding energies of nuclei. A zero-mode quantization of the Skyrmion is performed in the truncated BPS theory and the results are compared to the physical properties of the nucleon. The approach is an analogue in five-dimensional Minkowski spacetime of a recent holographic construction of a Skyrme model by Sakai and Sugimoto, based on a string theory derivation of a Yang-Mills-Chern-Simons theory in a curved five-dimensional spacetime.