Crystals of gauged solitons, force free plasma and resurgence

TL;DR

This paper presents analytic solutions of gauged solitons with crystalline structures in a (3+1)-dimensional non-linear sigma model, revealing force free plasma behavior, resurgent properties, and band spectra modulated by parameters.

Contribution

It introduces novel gauged soliton solutions with crystalline structures and force free plasma characteristics, connecting non-integrable theory perturbations to resurgence phenomena.

Findings

Gauged solitons exhibit crystalline structures supporting force free plasma.

Perturbations relate to Lamé operator and show resurgent behavior.

Numerical analysis reveals band-gap modulation by potential strength.

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.