Towards a classification of charge-3 monopoles with symmetry-Reference-Cited by-同舟云学术

Towards a classification of charge-3 monopoles with symmetry

Published:2023-07-28 Issue:4 Volume:113 Page:
ISSN:1573-0530
Container-title:Letters in Mathematical Physics
language:en
Short-container-title:Lett Math Phys

Author:

Braden H. W.^ORCID,Disney-Hogg Linden^ORCID

Abstract

AbstractWe classify all possible charge-3 monopole spectral curves with non-trivial automorphism group and within these identify those with elliptic quotients. By focussing on elliptic quotients the transcendental constraints for a monopole spectral curve become ones regarding periods of elliptic functions. We construct the Nahm data and new monopole spectral curves with

$$D_6$$

D 6 and

$$V_4$$

V 4 symmetry, the latter based on an integrable complexification of Euler’s equations, and for which energy density isosurfaces are plotted. Extensions of our approach to higher charge and hyperbolic monopoles are discussed.

Funder

Engineering and Physical Sciences Research Council

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://link.springer.com/content/pdf/10.1007/s11005-023-01708-5.pdf

Reference39 articles.

1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 10th printing, with corrections. National Bureau of Standards. A Wiley-Interscience Publication. New York etc.: Wiley. xiv, 1046 pp. £ 42.70 (1972) (1972)

2. Armstrong, J.A., Bloembergen, N., Ducuing, J., Pershan, P.S.: Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939 (1962)

3. Atiyah, M.F.: Magnetic monopoles in hyperbolic spaces. In: Vector bundles on Algebraic varieties, pp. 1–29 (1984)

4. Atiyah, M.F., Hitchin, N.J.: The Geometry and Dynamics of Magnetic Monopoles. Princeton University Press, Princeton (1988)

5. Berndt, B.C., Bhargava, S., Garvan, F.G.: Ramanujan’s theories of elliptic functions to alternative bases. Trans. Am. Math. Soc. 347(11), 4163–4244 (1995)