Abstract
The topological invariants of monopoles are described for an arbitrary compact gauge groupG and Higgs fieldΦ in any representation. The results generalize those obtained recently for compact and simply connectedG andΦ in the adjoint representation. The cases when the residual symmetry group isH=U(1) orH=U(3) are worked out explicitly. This latter is needed to accommodate fractional electric charge with monopoles having one Dirac unit magnetic charge.
The general theory is illustrated on the SU(5) monopole.
Similar content being viewed by others
References
Horváthy, P. A., Rawnsley, J. H.: Topological charges in monopole theories. Commun. Math. Phys.96, 497 (1984)
Taubes, C. H.: Surface integrals and monopole charges in non-Abelian gauge theories. Commun. Math. Phys.81, 299 (1981)
Schwarz, A. S.: Magnetic monopoles in gauge theories. Nucl. Phys.B112, 358 (1976)
Goddard. P., Olive, D. I. Charge quantization in theories with an adjoint representation Higgs mechanism. Nucl. Phys.B191, 511 (1981)
Humphreys, J. E.: Introduction to Lie algebras and representation theory. Berlin, Heidelberg, New York: Springer 1972
Wallach, N. R.: Harmonic analysis on homogeneous spaces, New York: Marcel Dekker 1973
Kobayashi, S., Nomizu, K.: Foundations of differential geometry Vol. I. and Vol. II. New York: Interscience 1963 and 1969
Weinberg, E. J.: Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups. Nucl. Phys.B167, 500 (1980)
Weinberg, E. J.: Fundamental monopoles in theories with arbitrary symmetry breaking. Nucl. Phys.B203, 445 (1982)
Corrigan, E., Olive, D. I.: Colour and magnetic monopoles. Nucl. Phys.B110, 237 (1976)
Georgi, H., Glashow, S.L.: Unity of all elementary-particle forces. Phys. Rev. Lett.32, 438 (1974)
Dokos, C. P., Tomaras, T. N.: Monopoles and dyons in the SU(5) model. Phys. Rev.D21, 2940 (1980)
Daniel, M., Lazarides, G., Shafi, Q.: SU(5) monopoles, magnetic symmetry and confinement. Nucl. Phys.B170, [FS1], 156 (1980)
Coleman, S.: The magnetic monopole fifty years later, In: Proc. E. Majorana Summer School, 1981 Harvard Univ. Preprint No HUTP-82/A032
Goddard, P., Nuyts, J., Olive, D.: Gauge theories and magnetic charge. Nucl. Phys.B125, 1 (1977)
O'Raifearetaigh, L.: private communication
Kirillov, A.: Eléments de la théorie des représentations Moscou: MIR (1974)
Kostant, B.: Quantization and Unitary representations. In: Lecture Notes in Math. Vol.170, Berlin, Heidelberg, New York: Springer 1970
Souriau, J-M.: Structure des systèmes dynamiques Paris: Dunod 1970
Forgács, P., Horváth, Z., Palla, L.: On the construction of axially symmetric SU(N) monopoles. Nucl. Phys.B221, 235 (1983)
Horváth, Z., Palla, L.: Monopoles and grand unification theories. Phys. Lett69B, 197 (1977)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Rights and permissions
About this article
Cite this article
Horváthy, P.A., Rawnsley, J.H. Monopole charges for arbitrary compact gauge groups and Higgs fields in any representation. Commun.Math. Phys. 99, 517–540 (1985). https://doi.org/10.1007/BF01215908
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01215908