The general caloron correspondence

2011/05/31 by Pedram Hekmati, Michael K. Murray, Raymond F. Vozzo · 1 citation
Mathematics · Physics and Astronomy · #Automorphism #Black Holes and Theoretical Physics #Characteristic class #Connection (principal bundle) #Gauge (firearms) #Geometry #Geometry and complex manifolds #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Mathematics #Physics #Principal bundle #Pure mathematics #Quantum mechanics #Vector bundle #hep-th #math.DG #msc:22E65 #msc:22E67 #msc:55R10 #msc:55R91

paper · pdf · doi:10.1016/j.geomphys.2011.10.015

published as J. Geom. Phys., 62(2):224-241, 2012 · 25 pages. New section added containing examples

arxiv created 2011/06/26 · openalex publication_date 2011/10/31 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We outline in detail the general caloron correspondence for the group of automorphisms of an arbitrary principal G-bundle Q over a manifold X, including the case of the gauge group of Q. These results are used to define characteristic classes of gauge group bundles. Explicit but complicated differential form representatives are computed in terms of a connection and Higgs field.

Citations

• The inverse function theorem of Nash and Moser
• Loop groups, Kaluza-Klein reduction and M-theory

Cited by

• Equivariant, string and leading order characteristic classes associated to fibrations

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• The Chern Character of Certain Infinite Rank Bundles arising in Gauge Theory
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