We construct topological soliton solutions describing baryonic tubes and layers with modulation in the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> non-linear sigma model coupled with ω-mesons in <math><mn>3</mn><mo>+</mo><mn>1</mn></math> dimensions. Using appropriate Ansäntze for the pionic matter field and the ω-mesons vector potential, the complete set of seven coupled partial differential equations can be solved analytically. These solutions represent modulated tubes and layers at finite volume with arbitrary baryon number, where the modulation of the solitons in one direction is determined by one of the three degrees of freedom of the pionic field, satisfying the equation of a two-dimensional free massless chiral scalar field. As expected, the inclusion of the ω-mesons to the non-linear sigma model allows to reduce the repulsion energy between baryons, which leads to a flattening of the tubes and layers in one direction, forming a kind of “nuclear linguine phase”. Also, we show that this construction can be carried out even when higher order terms in the large <math><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></math> expansion are included -in particular the Skyrme term- without spoiling the integrability of the field equations.

Chile

Gonzalo Barriga

Italy

Matías Torres

Aldo Vera

Exact modulated hadronic tubes and layers at finite volume in a cloud of And Mesons

In this work we analize how the inclusion of extra mesonic degrees of freedom affect the finite density solitons crystals of the Skyrme model. In particular, the first analytic examples of hadronic crystals at finite baryon density in both the Skyrme ω-mesons model as well as for the Skyrme ρ-mesons theory are constructed. These configurations have arbitrary topological charge and describe crystals of baryonic tubes surrounded by a cloud of vector-mesons. In the ω-mesons case, it is possible to reduce consistently the complete set of seven coupled non-linear field equations to just two integrable differential equations; one ODE for the Skyrmion profile and one PDE for the ω-mesons field. This analytical construction allows to show explicitly how the inclusion of ω-mesons in the Skyrme model reduces the repulsive interaction energy between baryons. In the Skyrme ρ-mesons case, it is possible to construct analytical solutions using a meron-type ansatz and fixing one of the couplings of the ρ-mesons action in terms of the others. We show that, quite remarkably, the values obtained for the coupling constants by requiring the consistency of our ansatz are very close to the values used in the literature to reduce nuclei binding energies of the Skyrme model without vector-mesons. Moreover, our analytical results are in qualitative agreement with the available results on the nuclear spaghetti phase.

Fabrizio Canfora

Marcela Lagos

On the robustness of solitons crystals in the Skyrme model

We show that the (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional gauged nonlinear sigma model minimally coupled to a <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> gauge field possesses analytic solutions representing gauged solitons at finite baryon density whose electromagnetic field is a force-free plasma. These gauged solitons manifest a crystalline structure and generate in a very natural way persistent currents able to support force-free plasma electromagnetic fields. The trajectories of charged test particles moving within these configurations can be characterized. Quite surprisingly, despite the nonintegrable nature of the theory, some of the perturbations of these gauged solitons allow one to identify a proper resurgent parameter. In particular, the perturbations of the solitons profile are related to the Lamé operator. On the other hand, the electromagnetic perturbations on the configurations satisfy a two-dimensional effective Schrödinger equation, where the soliton’s background interacts with the electromagnetic perturbations through an effective two-dimensional periodic potential. We studied numerically the band energy spectrum for different values of the free parameters of the theory and we found that band gaps are modulated by the potential strength. Finally we compare our crystal solutions with those of the (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional Gross-Neveu model.