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Gauged Sigma Models and Magnetic Skyrmions
by Bernd J Schroers
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Submission summary
| Authors (as registered SciPost users): | Bernd Schroers |
| Submission information | |
|---|---|
| Preprint Link: | scipost_201905_00004v3 (pdf) |
| Date accepted: | 2019-08-28 |
| Date submitted: | 2019-07-30 02:00 |
| Submitted by: | Schroers, Bernd |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author comments upon resubmission
List of changes
1. The introduction is substantially re-written and extended to bring out clearly that this paper goes far beyond the earlier paper [8] (in the new ordering of references), both in terms of applications (in deals with the most general DM interaction for magnetic skyrmions and includes impurities) and in terms of the underlying geometry (the underlying mathematical reason for solvability was not clear in [8] but is fully understood in this paper). The difference between this model and gauged non-linear sigma models studied elsewhere in the literature is also clarified.
2. I have made minor changes to Sections 2 (some more details on boundary terms in 2.4) and 3 (a new final section 3.3 to highlight the general formula for solutions). Despite the reservations the referees have expressed about the use of differential forms I have not replaced them. I find them by far the most efficient tools for the calculations in these sections, and rely on them to bring out the mathematical structures which underpin the model. This would be harder and less clear in traditional vector calculus notation. I would also make the case that this paper has a strong interdisciplinary element, connecting condensed matter physics with differential geometry and mathematical physics, and that some compromise in the notation is therefore inevitable. Finally, I have made only very minor use of differential forms in the new Section 4 which deals with applications.
3. I have introduced an entirely new Section 4 which spells out the application to magnetic skyrmions and impurities in much more detail then the previous version. This should bring out clearly the range of applications and also the extent to which the gauged sigma models provide a unifying picture for magnetic skyrmions and impurities.
4. The new version uses the SciPost style file, and this automatically adds a table of contents.
Published as SciPost Phys. 7, 030 (2019)