Abstract
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}^1right) ) 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 ϵ2. 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.
Highlights
Feature of having an infinite-dimensional moduli space for static solutions consisting of all volume-preserving diffeomorphism maps
Various theoretical and phenomenological studies have been done regarding the near-BPS Skyrme model [4,5,6,7,8] but a fundamental question still remains unanswered: when the non-BPS perturbations are gradually switched off, the solution in an arbitrary baryonic sector flows to a particular BPS solution, one of many in the infinite dimensional moduli space, but which one? Clearly, it is the infinite number of zero modes — the very same feature which makes the model attractive — that makes the question hard to answer, both analytically and numerically
We have studied the near-BPS regime of the baby Skyrme model with the standard pion mass term as the potential and the kinetic term as the BPS-breaking perturbation with coefficient
Summary
Skyrmion, has support on a compact domain in the limit of → 0 and is dubbed a compacton [16]. In this limit the model is called the BPS baby-Skyrme model or restricted baby-Skyrme model. In terms of which the nonlinear sigma model constraint φ · φ = 1 is manifest and we can write the Lagrangian components as. We will keep both formalisms in this paper, as ω is useful for analytical calculations and φ is useful for the numerical analysis
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