Kampmeijer, L. and Slingerland, J.K. and Schroers, B.J. and Bais, F.A.
Magnetic Charge Lattices, Moduli Spaces and Fusion Rules.
Nuclear Physics B, 806 (1/2).
We analyze the set of magnetic charges carried by smooth BPS monopoles in Yang-Mills-
Higgs theory with arbitrary gauge group G spontaneously broken to a subgroup H. The
charges are restricted by a generalized Dirac quantization condition and by an inequality
due to Murray. Geometrically, the set of allowed charges is a solid cone in the coroot lattice
of G, which we call the Murray cone. We argue that magnetic charge sectors correspond to
points in the Murray cone divided by the Weyl group of H; hence magnetic charge sectors
are labelled by dominant integral weights of the dual group H. We dene generators of the
Murray cone modulo Weyl group, and interpret the monopoles in the associated magnetic
charge sectors as basic; monopoles in sectors with decomposable charges are interpreted
as composite congurations. This interpretation is supported by the dimensionality of
the moduli spaces associated to the magnetic charges and by classical fusion properties for
smooth monopoles in particular cases. Throughout the paper we compare our ndings with
corresponding results for singular monopoles recently obtained by Kapustin and Witten.
||Preprint version of original article published in Nuclear Physics B, Vol.806 No.1/2(2009) © 2009 Elsevier B.V. All rights reserved. We are grateful to the Kavli Institute for Theoretical Physics for hospitality during a visit in
2006. LK thanks Ilies Messamah, Lotte Hollands, Tom Koornwinder and Jochen Heinloth for
helpful discussions. This work is part of the research programme of the 'Stichting voor Fundamenteel
Onderzoek der Materie (FOM)', which is nancially supported by the 'Nederlandse
Organisatie voor Wetenschappelijk Onderzoek (NWO)'.
||Non-abelian monopoles; Generating charges; Stratified moduli spaces; Parameter counting; Multi-monopole solutions; Dual gauge group;
||Science & Engineering > Mathematical Physics
Dr. Joost Slingerland
||27 Sep 2011 15:42
|Journal or Publication Title:
||Nuclear Physics B
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