Asymptotic Metrics for SU ( N )-Monopoles with Maximal Symmetry Breaking

1998/01/31 by Roger Bielawski · 3 citations
Mathematics · Medicine · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Geometry #Mathematical physics #Mathematics #Particle physics #Physics #Soft tissue tumor case studies #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Theoretical physics #hep-th

paper · pdf · doi:10.1007/s002200050503

published as Commun.Math.Phys. 199 (1998) 297-325 · 26 pages, AMS-Latex; comparison of metrics done differently and in greater detail; version submitted

arxiv created 1998/03/18 · openalex publication_date 1998/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We compute the asymptotic metrics for moduli spaces of SU(N) monopoles with maximal symmetry breaking. These metrics are exponentially close to the exact monopole metric as soon as, for each simple root, the individual monopoles corresponding to that root are well separated. We also show that the estimates can be differentiated term by term in natural coordinates, which is a new result even for SU(2) monopoles.

Citations

• Elliptic Partial Differential Equations of Second Order
• The Geometry and Dynamics of Magnetic Monopoles
• A Hyper-KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group

Cited by

• Line bundles on spectral curves and the generalised Legendre transform construction of hyperkähler metrics
• Wall crossing from Dirac zeromodes
• Super Yang-Mills theory with impurity walls and instanton moduli spaces