Ordered arrays of Baryonic tubes in the Skyrme model in (3+1) dimensions at finite density

TL;DR

This paper introduces a new ansatz for the Skyrme model in (3+1) dimensions that simplifies the equations and describes ordered arrays of baryonic tubes at finite density, revealing crystal-like structures with explicit energy density peaks.

Contribution

The authors present a novel ansatz reducing Skyrme field equations to a single solvable profile equation, enabling explicit solutions for ordered baryonic tube arrays at finite density.

Findings

Energy density peaks form a crystalline lattice of tubes.

Configurations exhibit periodic dependence on two spatial directions.

Solutions demonstrate stability and explicit peak positions.

Abstract

A consistent ansatz for the Skyrme model in (3+1)-dimensions which is able to reduce the complete set of Skyrme field equations to just one equation for the profile in situations in which the Baryon charge can be arbitrary large is introduced: moreover, the field equation for the profile can be solved explicitly. Such configurations describe ordered arrays of Baryonic tubes living in flat space-times at finite density. The plots of the energy density (as well as of the Baryon density) clearly show that the regions of maximal energy density have the shape of a tube: the energy density and the Baryon density depend periodically on two spatial directions while they are constant in the third spatial direction. Thus, these topologically non-trivial crystal-like solutions can be intepreted as configurations in which most of the energy density and the baryon density are concentrated within tube-shaped regions. The positions of the energy-density peaks can be computed explicitly and they manifest a clear crystalline order. A non-trivial stability test is discussed.