Gauged sigma models and magnetic Skyrmions

Schroers, Bernd

doi:10.21468/SciPostPhys.7.3.030

SciPost Physics

Gauged sigma models and magnetic Skyrmions

Bernd J Schroers

SciPost Phys. 7, 030 (2019) · published 10 September 2019

doi: 10.21468/SciPostPhys.7.3.030
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Abstract

We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary Dzyaloshinskii-Moriya interaction, for a suitably chosen gauge field. We use the interplay of unitary and holomorphic structures to derive a general solution of the first order Bogomol'nyi equation of the model for any given connection. We illustrate this formula with examples, and also point out applications to the study of impurities.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.7.3.030
TI  - Gauged sigma models and magnetic Skyrmions
PY  - 2019/09/10
UR  - https://scipost.org/SciPostPhys.7.3.030
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 7
IS  - 3
SP  - 030
A1  - Schroers, Bernd
AB  - We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary Dzyaloshinskii-Moriya interaction, for a suitably chosen gauge field. We use the interplay of unitary and holomorphic structures to derive a general solution of the first order Bogomol'nyi equation of the model for any given connection. We illustrate this formula with examples, and also point out applications to the study of impurities.
ER  -

@Article{10.21468/SciPostPhys.7.3.030,
	title={{Gauged sigma models and magnetic Skyrmions}},
	author={Bernd J Schroers},
	journal={SciPost Phys.},
	volume={7},
	pages={030},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.7.3.030},
	url={https://scipost.org/10.21468/SciPostPhys.7.3.030},
}

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Sigma models Skyrmions

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¹ ² Bernd Schroers