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Magnetic Charge Lattices, Moduli Spaces and Fusion Rules

Kampmeijer, L. and Slingerland, J.K. and Schroers, B.J. and Bais, F.A. (2009) Magnetic Charge Lattices, Moduli Spaces and Fusion Rules. Nuclear Physics B, 806 (1/2). pp. 386-435. ISSN 0550-3213

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Abstract

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.

Item Type: Article
Additional Information: 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)'.
Keywords: Non-abelian monopoles; Generating charges; Stratified moduli spaces; Parameter counting; Multi-monopole solutions; Dual gauge group;
Subjects: Science & Engineering > Mathematical Physics
Item ID: 2734
Identification Number: 10.1016/j.nuclphysb.2008.08.003
Depositing User: Dr. Joost Slingerland
Date Deposited: 27 Sep 2011 15:42
Journal or Publication Title: Nuclear Physics B
Publisher: Elsevier
Refereed: No
URI:

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