Crystals of gauged solitons, force-free plasma, and resurgence

We show that the (3 + 1)-dimensional gauged nonlinear sigma model minimally coupled to a U(1) 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 Lame operator. On the other hand, the electromagnetic perturbations on the configurations satisfy a two-dimensional effective Schrodinger 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 (1 + 1)-dimensional Gross-Neveu model.

Automated summary

The study demonstrates that the (3 + 1)-dimensional gauged nonlinear sigma model minimally coupled to a U(1) gauge field has analytic solutions representing gauged solitons with crystalline structures generating persistent currents at finite baryon density, where the electromagnetic field forms a force-free plasma. Despite the nonintegrable nature of the theory, perturbations of these gauged solitons allow the identification of a proper resurgent parameter, with some perturbations related to the Lame operator. The band energy spectrum for different theory parameters show modulated band gaps, with electromagnetic perturbations interacting with the soliton background through an effective two-dimensional periodic potential. Comparisons are made with crystal solutions of the (1 + 1)-dimensional Gross-Neveu model.