Near-BPS baby Skyrmions
Sven Bjarke Gudnason, Marco Barsanti, Stefano Bolognesi
Abstract
A bstract We consider the baby-Skyrme model in the regime close to the so-called restricted baby-Skyrme model, which is a BPS model with area-preserving diffeomorphism invariance. The perturbation takes the form of the standard kinetic Dirichlet term with a small coefficient ϵ . Classical solutions of this model, to leading order in ϵ , are called restricted harmonic maps. In the BPS limit ( ϵ → 0) of the model with the potential being the standard pion-mass term, the solution with unit topological charge is a compacton. Using analytical and numerical arguments we obtain solutions to the problem for topological sectors greater than one. We develop a perturbative scheme in ϵ with which we can calculate the corrections to the BPS mass. The leading order ( $$ \mathcal{O}\left({\upepsilon}^1\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>ϵ</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mfenced> </mml:math> ) corrections show that the baby Skyrmion with topological charge two is energetically preferred. The binding energy requires us to go to the third order in ϵ to capture the relevant terms in perturbation theory, however, the binding energy contributes to the total energy at order ϵ 2 . We find that the baby Skyrmions — in the near-BPS regime — are compactons of topological charge two, that touch each other on their periphery at a single point and with orientations in the attractive channel.