# Construction of Nahm data and BPS monopoles with continuous symmetries

@article{Charbonneau2022ConstructionON, title={Construction of Nahm data and BPS monopoles with continuous symmetries}, author={Benoit Charbonneau and Anuk Dayaprema and Craig J. Lang and {\'A}kos Nagy and Haoyang Yu}, journal={Journal of Mathematical Physics}, year={2022} }

We study solutions to Nahm’s equations with continuous symmetries and, under certain (mild) hypotheses, we classify the corresponding Ansätze. Using our classification, we construct novel Nahm data, and prescribe methods for generating further solutions. Finally, we use these results to construct new BPS monopoles with spherical symmetry. 1. Background and motivation When one studies a particular equation of interest and is confronted with the desire to prove the existence of solutions, the…

## References

SHOWING 1-10 OF 72 REFERENCES

Nahm data and SU(3) monopoles

- Mathematics
- 1992

A moduli space of Nahm data is shown to produce, via the ADHM-Nahm construction, SU(3) monopoles with minimal symmetry breaking. The author finds analytical and numerical expressions for the Higgs…

Nahm's equations and hyperkähler geometry

- Mathematics
- 1993

The geometry of certain moduli spaces of solutions to Nahm's equations is studied, and a family of gravitational instationsj is shown to arise as a deformation of theh Atiyah-Hitchin maniford.

A description of E. Weinberg's continuous family of monopoles using the Atiyah-Drinfeld-Hitchin-Manin-Nahm formalism

- Economics
- 1983

Cyclic Monopoles, Affine Toda and Spectral Curves

- Mathematics
- 2011

We show that any cyclically symmetric monopole is gauge equivalent to Nahm data given by Sutcliffe’s ansatz, and so obtained from the affine Toda equations. Further the direction (the Ercolani-Sinha…

Yang-Mills-Higgs monopole solutions of arbitrary topological charge

- Mathematics
- 1981

We propose a construction of static magnetic Yang-Mills-Higgs monopole solutions of arbitrary topological charge. They are axially symmetric and contain no free parameters except for their position.…

On the Constraints Defining BPS Monopoles

- Mathematics
- 1999

Abstract: We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We…

On the Tetrahedrally Symmetric Monopole

- Mathematics
- 2009

We study SU(2) BPS monopoles with spectral curves of the form η3+χ(ζ6+bζ3−1) = 0. Previous work has established a countable family of solutions to Hitchin’s constraint that L2 was trivial on such a…

SU(N) monopoles and Platonic symmetry

- Physics
- 1997

We discuss the ADHMN construction for SU(N) monopoles and show that a particular simplification arises in studying charge N−1 monopoles with minimal symmetry breaking. Using this we construct…