The vector BPS baby Skyrme model

TL;DR

This paper explores the relationship between the BPS baby Skyrme model and its vector meson formulation, revealing how potential choices influence soliton solutions and stability, with implications for understanding topological solitons.

Contribution

It demonstrates how different potentials affect the existence and stability of solitons in the vector baby Skyrme model, highlighting the impact of potential form on solution spectrum.

Findings

Compactons disappear in the vector model without a source term.

Exponential solitons exist for squared potential, saturating a nonlinear BPS bound.

Higher solitons are unstable due to nonlinear BPS bounds.

Abstract

We investigate the relation between the BPS baby Skyrme model and its vector meson formulation, where the baby Skyrme term is replaced by a coupling between the topological current $B_\mu$ and the vector meson field $\omega_\mu$. The vector model still possesses infinitely many symmetries leading to infinitely many conserved currents which stand behind its solvability. It turns out that the similarities and differences of the two models depend strongly on the specific form of the potential. We find, for instance, that compactons (which exist in the BPS baby Skyrme model) disappear from the spectrum of solutions of the vector counterpart. Specifically, for the vector model with the old baby Skyrme potential we find that it has compacton solutions only provided that a delta function source term effectively screening the topological charge is inserted at the compacton boundary. For the old baby Skyrme potential squared we find that the vector model supports exponentially localized solitons, like the BPS baby Skyrme model. These solitons, however, saturate a BPS bound which is a nonlinear function of the topological charge and, as a consequence, higher solitons are unstable w.r.t. decay into smaller ones, which is at variance with the more conventional situation (a linear BPS bound and stable solitons) in the BPS baby Skyrme model.