TY - JOUR

T1 - A model for gauged skyrmions with low binding energies

AU - Cork, Josh

AU - Harland, Derek

AU - Winyard, Thomas

N1 - Funding Information: JC is grateful to Lancaster University, UK, for allowing extended access to MATLAB, through which many of the results of this work were calculated. TW was supported by the University of Leeds as an Academic Development Fellow throughout the duration of this project, and by the UK Engineering and Physical Sciences Research Council through grant EP/P024688/1. Some of the numerical simulations were run using the Soliton Solver library developed by TW at the University of Leeds. This work was undertaken on ARC4, part of the High Performance Computing facilities at the University of Leeds, UK.

PY - 2022/1/7

Y1 - 2022/1/7

N2 - We consider gauged skyrmions with boundary conditions which break the gauge from SU(2) to U(1) in models derived from Yang-Mills theory. After deriving general topological energy bounds, we approximate charge 1 energy minimisers using KvBLL calorons with non-trivial asymptotic holonomy, use them to calibrate the model to optimise the ratio of energy to lower bound, and compare them with solutions to full numerical simulation. Skyrmions from calorons with non-trivial asymptotic holonomy exhibit a non-zero magnetic dipole moment, which we calculate explicitly, and compare with experimental values for the proton and the neutron. We thus propose a way to develop a physically realistic Skyrme-Maxwell theory, with the potential for exhibiting low binding energies.

AB - We consider gauged skyrmions with boundary conditions which break the gauge from SU(2) to U(1) in models derived from Yang-Mills theory. After deriving general topological energy bounds, we approximate charge 1 energy minimisers using KvBLL calorons with non-trivial asymptotic holonomy, use them to calibrate the model to optimise the ratio of energy to lower bound, and compare them with solutions to full numerical simulation. Skyrmions from calorons with non-trivial asymptotic holonomy exhibit a non-zero magnetic dipole moment, which we calculate explicitly, and compare with experimental values for the proton and the neutron. We thus propose a way to develop a physically realistic Skyrme-Maxwell theory, with the potential for exhibiting low binding energies.

KW - calorons

KW - gauged skyrmions

KW - topological bounds

KW - Yang-Mills theory

UR - http://www.scopus.com/inward/record.url?scp=85122886414&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ac3c81

DO - 10.1088/1751-8121/ac3c81

M3 - Article

AN - SCOPUS:85122886414

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 1

M1 - 015204

ER -