Communications in Mathematical Physics

, Volume 86, Issue 3, pp 437–448 | Cite as

Deformations of the embedding of the SU(2) monopole solution in SU (3)

  • R. S. Ward


This paper is concerned with static Yang-Mills-Higgs fields, in the Prasad-Sommerfield limit of no Higgs self-interaction. One can obtain SU (3) multipole solutions from SU(2) solutions by embedding, in several different ways. In some of these cases, the embedding belongs to a family of SU(3) solutions that are not all embeddings; in other words, some embeddings can be deformed into non-embeddings. The simplest case, an embedding of the SU(2) spherically symmetric monopole, is studied with the aid of the twistor construction procedure. The family of axially symmetric SU(3) solutions to which it belongs is described.


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  1. 1.
    Ward, R.S.: A Yang-Mills-Higgs monopole of charge 2. Commun. Math. Phys.79, 317–325 (1981)Google Scholar
  2. 2.
    Prasad, M.K.: Yang-Mills-Higgs monopole solutions of arbitrary topological charge. Commun. Math. Phys.80, 137–149 (1981)Google Scholar
  3. 3.
    Ward, R.S.: Two Yang-Mills-Higgs monopoles close together. Phys. Lett.102B, 136–138 (1981)Google Scholar
  4. 4.
    Corrigan, E., Goddard, P.: Ann monopole solution with 4n-1 degrees of freedom. Commun. Math. Phys.80, 575–587 (1981)Google Scholar
  5. 5.
    Hitchin, N.J.: Monopoles and geodesics. Commun. Math. Phys.83, 579–602 (1982)Google Scholar
  6. 6.
    Taubes, C.H.: The existence of multi-monopole solutions to the non-Abelian, Yang-Mills-Higgs equations for arbitrary simple gauge groups. Commun. Math. Phys.80, 343–367 (1981)Google Scholar
  7. 7.
    Weinberg, E.J.: Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups. Nucl. Phys. B167, 500–524 (1980)Google Scholar
  8. 8.
    Ward, R.S.: Magnetic monopoles with gauge group SU(3) broken to U(2). Phys. Lett.107B, 281–284 (1981)Google Scholar
  9. 9.
    Athorne, C.: Cylindrically and spherically symmetric monopoles in SU(3) gauge theory. Preprint, DurhamGoogle Scholar
  10. 10.
    Jaffe, A., Taubes, C.: Vortices and monopoles. Boston: Birkhäuser 1980Google Scholar
  11. 11.
    Goddard, P., Nuyts, J., Olive, D.: Gauge theories and magnetic charge. Nucl. Phys. B125, 1–28 (1977)Google Scholar
  12. 12.
    Wilkinson, D., Bais, F.A.: Exact SU(n) monopole solutions with spherical symmetry. Phys. Rev. D19, 2410–2415 (1979)Google Scholar
  13. 13.
    Bais, F.A., Weldon, H.A.: Exact monopole solutions in SU(n) gauge theory. Phys. Rev. Lett.41, 601–604 (1978)Google Scholar
  14. 14.
    Corrigan, E.F., Fairlie, D.B., Yates, R.G., Goddard, P.: The construction of self-dual solutions to SU(2) gauge theory. Commun. Math. Phys.58, 223–240 (1978)Google Scholar
  15. 15.
    Ward, R.S.: Ansätze for self-dual Yang-Mills Fields. Commun. Math. Phys.80, 563–574 (1981)Google Scholar
  16. 16.
    Weinberg, E.J.: Fundamental monopoles in theories with arbitrary symmetry breaking. Preprint, Columbia University, 1982Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • R. S. Ward
    • 1
  1. 1.Institute for Theoretical PhysicsState University of New York at Stony Brook, Stony BrookNew YorkUSA

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