Monopoles and the Gibbons-Manton Metric

1998/01/14 by Roger Bielawski · 5 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Fisher information metric #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Injective metric space #Magnetic monopole #Manifold (fluid mechanics) #Metric (unit) #Moduli space #Torus #Twistor space #Twistor theory #hep-th

paper · pdf · doi:10.1007/s002200050359

published as Commun.Math.Phys. 194 (1998) 297-321 · 24 pages, AMS-Latex, to appear in Commun. Math. Phys

arxiv created 1998/01/14 · openalex publication_date 1998/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that, in the region where monopoles are well separated, the L²-metric on the moduli space of n-monopoles is exponentially close to the Tⁿ-invariant hyperkähler metric proposed by Gibbons and Manton. The proof is based on a description of the Gibbons-Manton metric as a metric on a certain moduli space of solutions to Nahm's equations, and on twistor methods. In particular, we show how the twistor description of monopole metrics determines the asymptotic metric.

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