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.
Repository Staff Only(login required)
||Item control page