On the effects of the Chern-Simons term in an Abelian gauged Skyrme model in d = 4 + 1 dimensions

Francisco Navarro-Lérida,Eugen Radu,D.H Tchrakian

doi:10.1016/j.physletb.2021.136083

Francisco Navarro-Lérida, Eugen Radu + Show 1 more

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https://doi.org/10.1016/j.physletb.2021.136083

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Abstract

We study an Abelian gauged O(5) Skyrme model in 4+1 dimensions, featuring the F4 Maxwell and the Chern-Simons terms. Our aim is to expose the mechanism, discovered in the analogous Abelian gauged O(3) Skyrme model in 2+1 dimensions, which leads to the unusual relation of the mass-energy E to the electric charge Qe and angular momentum J, and, to the change in the value of the “baryon number” q due to the influence of the Abelian field on the Skyrmion. Chern-Simons dynamics together with the dynamics of the gauged Skyrme scalar, allows for solutions with varying asymptotic values of the magnetic field, resulting in these unusual properties listed. Numerical work is carried out on an effective one dimensional subsystem resulting from imposition of an enhanced radial symmetry on R4.

Highlights

The Skyrme model has started almost sixty years ago [1,2], providing the very first explicit example of solitons in a relativistic non-linear field theory in d = 3 + 1 spacetime dimensions
Like the baryon number density prior to gauging, say 0, its gauge-deformed counterpart is by construction essentially total divergence, meaning that in a constraint-compliant parametrisation of the Skyrme scalar it is total divergence
The main purpose of this work was to expose the mechanism leading to several new unusual features discovered in the Abelian gauged O (3) Skyrme model with a Chern-Simons term in 2 + 1 dimensions, which were reported in Ref. [10]

Summary

Introduction

The Skyrme model has started almost sixty years ago [1,2], providing the very first explicit example of solitons in a relativistic non-linear field theory in d = 3 + 1 spacetime dimensions This model has been generalised subsequently to all spacetime dimensions. Like the baryon number density prior to gauging, say 0, its gauge-deformed counterpart is by construction essentially total divergence, meaning that in a constraint-compliant parametrisation of the Skyrme scalar it is total divergence. This property enables the evaluation of the lower bound of the energy as a surface integral determined only by the asymptotic values of the solution, provided it is regular at the origin. It may be reasonable to call q a “gauge-deformed baryon number”

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