Abstract
We show that the (3+1)-dimensional gauged non-linear 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 non-integrable nature of the theory, some of the perturbations of these gauged solitons allow to identify a proper resurgent parameter. In particular, the perturbations of the solitons profile are related to the Lam\'e operator. On the other hand, the electromagnetic perturbations on the configurations satisfy a two-dimensional effective Schrodinger equation, where the soliton 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 bands-gaps are modulated by the potential strength. Finally we compare our crystal solutions with those of the (1+1)- dimesional Gross-Neveu model.
Highlights
One of the most important types of plasma in plasma physics is the so-called force-free plasma (FFP ), and several reasons justify this statement
We show that the (3 þ 1)-dimensional gauged nonlinear sigma model minimally coupled to a Uð1Þ gauge field possesses analytic solutions representing gauged solitons at finite baryon density whose electromagnetic field is a force-free plasma
FFPs are extremely relevant in many astrophysical situations
Summary
One of the most important types of plasma in plasma physics is the so-called force-free plasma (FFP ), and several reasons justify this statement. The gauged solitons constructed in [52,53] live at finite baryon density, and most of the energy and the topological charge are contained within tubeshaped regions which are regularly spaced These structures are expected in the description of cold and dense nuclear matter as a function of topological charge, commonly called nuclear pasta, and are quite relevant in the phase diagram of the low energy limit of QCD (see [56,57]). We will show that the electromagnetic field generated by the soliton crystals found in [51,52] (which describe quite well many features of the nuclear spaghetti phase) is of force-free type This connection between FFP and the nuclear pasta phase is a quite surprising result which (to the best of our knowledge) has not been discussed previously in the literature.
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