Gauged multisoliton baby Skyrme model

A Samoilenka,Ya Shnir

doi:10.1103/physrevd.93.065018

A Samoilenka, Ya Shnir

Open Access

https://doi.org/10.1103/physrevd.93.065018

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Abstract

We present a study of $U(1)$ gauged modification of the 2+1 dimensional planar Skyrme model with a particular choice of the symmetry breaking potential term which combines a short-range repulsion and a long-range attraction. In the absence of the gauge interaction the multi-solitons of the model are aloof, they consist of the individual constituents which are well separated. Peculiar feature of the model is that there are usually several different stable static multi-soliton solutions of rather similar energy in a topological sector of given degree. We investigated the pattern of the solutions and find new previously unknown local minima. It is shown that coupling of the aloof planar multi-Skyrmions to the magnetic field strongly affects the pattern of interaction between the constituents. We analyse the dependency of the structure of the solutions, their energies and magnetic fluxes on the strength of the gauge coupling. It is found that, generically, in the strong coupling limit the coupling to the gauge field results in effective recovering of the rotational invariance of the configuration.

Highlights

The study of topological solitons in field theory can be traced back to the seminal paper by Skyrme [1] where SU (2)-valued non-linear model for atomic nuclei was suggested
The Skyrme model can be derived from the expansion of the QCD low energy effective Lagrangian in the large Nc limit [2], the topological charge of the multisoliton configuration is set into correspondence to the physical baryon number
We study numerically the dependence of masses of these configurations and the corresponding magnetic fluxes on the gauge coupling constant, both in perturbative limit and in the strong coupling limit without any restrictions of symmetry

Summary

Introduction

The study of topological solitons in field theory can be traced back to the seminal paper by Skyrme [1] where SU (2)-valued non-linear model for atomic nuclei was suggested. The baby Skyrme model has a number of applications on its own, e.g., in condensed matter physics where Skyrmion configurations were observed experimentally [17], in the description of the topological quantum Hall effect [18, 19], or in brane cosmology where the solitons of the model induce warped compactification of the 2-dimensional extra space [20]. Stituents of the planar Skyrmions, each of them being associated with a fractional part of the topological charge of the configuration [28] Another possibility is to combine a short-range repulsion and a long-range attraction between the solitons [29, 30]. Analysis of the gauged baby Skyrmions [23] reveals very interesting features of the corresponding solutions which carry a non-quantized non-topological magnetic flux. We study numerically the dependence of masses of these configurations and the corresponding magnetic fluxes on the gauge coupling constant, both in perturbative limit and in the strong coupling limit without any restrictions of symmetry

The model

Numerical results

E dE dt

Findings

Conclusion