The Skyrme model in the BPS limit

TL;DR

The BPS Skyrme model offers a promising effective framework for nuclear physics, accurately describing nuclei, nuclear matter, and neutron stars with analytical insights and good observational agreement.

Contribution

This review highlights the BPS Skyrme model's unique features, including zero classical binding energies and a perfect fluid description, emphasizing its potential as a low-energy QCD effective model.

Findings

Zero classical binding energies for solitons

Analytical calculation of nuclear binding energies

Good agreement with neutron star observations

Abstract

In this review, we summarise the main features of the BPS Skyrme model which provides a physically well-motivated idealisation of atomic nuclei and nuclear matter: 1) it leads to zero binding energies for classical solitons (while realistic binding energies emerge owing to the semiclassical corrections, the Coulomb interaction and isospin breaking); 2) it describes a perfect non-barotropic fluid already at the microscopic (field theoretical) level which allows to study thermodynamics beyond the mean-field limit. These properties allow for an approximate but analytical calculation of binding energies of the most abundant nuclei, for a determination of the equation of state of skyrmionic matter (both in the full field theory and in a mean-field approximation) as well as the description of neutron stars as Skyrme solitons with a very good agreement with available observational data. All these results suggest that the proper low energy effective model of QCD should be close to the BPS Skyrme model in a certain sense (a "near-BPS Skyrme model"), with a prominent role played by the BPS part.