Quantization condition for 't Hooft monopoles in compact simple Lie groups

Englert, François; Windey, Paul

doi:10.1103/physrevd.14.2728

Cited by 85 publications

(99 citation statements)

References 7 publications

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“…There is, however, another consistency condition [21]. Note that a single valued gauge transformation on the equator defines a closed curve in H as well as in G, starting and ending at the unit element.…”

Section: Quantization Condition For Smooth Monopolesmentioning

confidence: 99%

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Magnetic charge lattices, moduli spaces and fusion rules

et al. 2009

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We analyze the set of magnetic charges carried by smooth BPS monopoles in Yang-MillsHiggs 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 define 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 configurations. 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 findings with corresponding results for singular monopoles recently obtained by Kapustin and Witten.

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Section: Quantization Condition For Smooth Monopolesmentioning

confidence: 99%

“…The magnetic charge of a singular monopole is restricted by the generalized Dirac quantization condition [21,1]. This consistency condition can be derived from the bundle description [20].…”

Section: Quantization Condition For Singular Monopolesmentioning

confidence: 99%

Magnetic charge lattices, moduli spaces and fusion rules

et al. 2009

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“…However, given a gauge group, G, not all flux sectors are permitted [4]; the electric fluxes, e, are in the weight lattice of the group G (modulo the root lattice of G): 28) and the magnetic fluxes,m, are in the weight lattice of the dual groupĜ (modulo the root lattice ofĜ, and up to a normalization if G is not simply-laced):…”

Section: The Partition Function and Electric-magnetic Dualitymentioning

confidence: 99%

“…[4]: in general, the duality g → 4π/g transforms the gauge group G into another group (the magnetic group) G, whose weight lattice is dual to the weight lattice of G.…”

Section: Introductionmentioning

confidence: 99%

S-duality in N = 4 Yang-Mills theories with general gauge groups

Girardello¹,

Giveon

Porrati

et al. 1995

Nuclear Physics B

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ABSTRACT't Hooft construction of free energy, electric and magnetic fluxes, and of the partition function with twisted boundary conditions, is extended to the case of N = 4 supersymmetric Yang-Mills theories based on arbitrary compact, simple Lie groups.The transformation of the fluxes and the free energy under S-duality is presented. We consider the partition function of N = 4 for a particular choice of boundary conditions, and compute exactly its leading infrared divergence. We verify that this partition function obeys the transformation laws required by S-duality. This provides independent evidence in favor of S-duality in N = 4 theories.

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“…The topological quantization condition requires that [5] Q M = 4π e r a=1 k a β a β 2 a · H (1. 4) with the k a all being integers; for self-dual BPS solutions these will all be positive.…”

Section: Introductionmentioning

confidence: 99%

Multicloud solutions with massless and massive monopoles

Houghton

Weinberg

2002

Phys. Rev. D

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Certain spontaneously broken gauge theories contain massless magnetic monopoles. These are realized classically as clouds of non-Abelian fields surrounding one or more massive monopoles. In order to gain a better understanding of these clouds, we study BPS solutions with four massive and six massless monopoles in an SU(6) gauge theory. We develop an algebraic procedure, based on the Nahm construction, that relates these solutions to previously known examples. Explicit implementation of this procedure for a number of limiting cases reveals that the six massless monopoles condense into four distinct clouds, of two different types. By analyzing these limiting solutions, we clarify the correspondence between clouds and massless monopoles, and infer a set of rules that describe the conditions under which a finite size cloud can be formed. Finally, we identify the parameters entering the general solution and describe their physical significance. *

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Quantization condition for 't Hooft monopoles in compact simple Lie groups

Cited by 85 publications

References 7 publications

Magnetic charge lattices, moduli spaces and fusion rules

Magnetic charge lattices, moduli spaces and fusion rules

S-duality in N = 4 Yang-Mills theories with general gauge groups

Multicloud solutions with massless and massive monopoles

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