"Half a proton" in the Bogomol'nyi-Prasad-Sommerfield Skyrme model

TL;DR

This paper explores the BPS Skyrme model, showing that it admits solutions with localized charge and energy densities, where parts of the solution can be spatially separated without interaction, highlighting unique symmetry properties.

Contribution

It demonstrates the existence of solutions with localized and separated charge and energy densities in the BPS Skyrme model, revealing new insights into its soliton configurations.

Findings

Localized charge and energy densities can be spatially separated.

Solutions exhibit invariance under volume-preserving diffeomorphisms.

A fraction of the solution's charge and energy can be far apart without interaction.

Abstract

The BPS Skyrme model is a model containing an $SU(2)$-valued scalar field, in which a Bogomol'nyi-type inequality can be satisfied by soliton solutions. In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group $SU(2)$ on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here, that in the BPS Skyrme model such solutions exists, that a fraction of their charge and energy densities are localised, and the remaining part can be any far away, not interacting with the localised part.