Rotationally invariant isospinning baby-skyrmions dressed by fermions

TL;DR

This paper investigates the coupling of Fermions to isospinning baby-skyrmions, revealing conditions for localized solutions, eigenstates, and the impact of Fermionic backreaction on the solitons.

Contribution

It introduces a method to find rotationally invariant Fermionic solutions in the baby-skyrme model with backreaction, including a novel isospin frequency constraint.

Findings

Localized Fermionic solutions exist with specific isospin frequencies.

Fermionic solutions are not generally Hamiltonian eigenstates, but become so in a certain limit.

Backreaction of Fermions significantly influences baby-skyrmion properties.

Abstract

We couple Fermions to the isospinning (2+1) baby-skyrme model. We show that consistent rotationally invariant localised solutions can be found but the Fermionic solutions to the equations of motion are not in general eigenstates of the Hamiltonian. These do however become full eigenstates in a particular limit. We also find the corresponding Fermionic eigenstates of the Hamiltonian, for which our Fermion ansatz is also well suited. For localised Fermionic states, a novel constraint on the internal isospin frequency exists. Throughout our studies, we include the backreaction of the Fermions on the baby-skyrmion.