The BPS sectors of the Skyrme model and their non-BPS extensions

TL;DR

This paper analyzes two BPS submodels of the Skyrme model, exploring their geometric, thermodynamic, and non-BPS extensions, providing analytical insights into Skyrmion properties and explaining the rational map ansatz's effectiveness.

Contribution

It offers a geometric formulation of BPS submodels, studies their thermodynamics, extends one to a non-BPS model with analytical solutions, and explains the rational map ansatz's success.

Findings

High-pressure equations of state match $p=\bar{\rho}/3$.

Matter in the first BPS submodel resembles a Bose-Einstein condensate.

Non-BPS extension retains the ansatz, enabling analytical Skyrmion profiles.

Abstract

Two recently found coupled BPS submodels of the Skyrme model are further analyzed. Firstly, we provide a geometrical formulation of the submodels in terms of the eigenvalues of the strain tensor. Secondly, we study their thermodynamical properties and show that the mean-field equations of state coincide at high pressure and read $p=\bar{\rho}/3$. We also provide evidence that matter described by the first BPS submodel has some similarity with a Bose-Einstein condensate. Moreover, we show that extending the second submodel to a non-BPS model by including certain additional terms of the full Skyrme model does not spoil the respective ansatz, leading to an ordinary differential equation for the profile of the Skymion, for any value of the topological charge. This allows for an almost analytical description of the properties of Skyrmions in this model. In particular, we analytically study the breaking and restoration of the BPS property. Finally, we provide an explanation of the success of the rational map ansatz.