The caloron correspondence and higher string classes for loop groups

2009/11/23 by Michael K. Murray, Raymond F. Vozzo
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Characteristic class #Class (philosophy) #Cohomology #Combinatorics #Computer science #Homotopy and Cohomology in Algebraic Topology #Lie group #Linguistics #Loop (graph theory) #Loop group #Loop space #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Space (punctuation) #String (physics) #hep-th #math.DG #msc:55R10 #msc:55R35 #msc:57R20 #msc:81T30

paper · pdf · doi:10.1016/j.geomphys.2010.04.010

published as J. Geom. Phys. 60:1235-1250, 2010 · 21 pages. Author addresses added

arxiv created 2009/11/23 · openalex publication_date 2010/04/26 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We review the caloron correspondence between G-bundles on M × S¹ and ΩG-bundles on M, where ΩG is the space of smooth loops in the compact Lie group G. We use the caloron correspondence to define characteristic classes for ΩG-bundles, called string classes, by transgression of characteristic classes of G-bundles. These generalise the string class of Killingback to higher dimensional cohomology.

Citations

• Chern-Weil calculus extended to a class of infinite dimensional manifolds
• The inverse function theorem of Nash and Moser
• Characteristic Forms and Geometric Invariants