2005/03/16 by Katrin Wehrheim, Wehrheim, Katrin
Mathematics · Physics and Astronomy · #53C07 #57Rxx #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories #math-ph #math.DG #math.MP #msc:53C07 #msc:57Rxx
paper · pdf · doi:10.48550/arxiv.math/0503341
6 pages, short version of an earlier note on my homepage
arxiv created 2005/03/16 · openalex publication_date 2005/03/16 · arxiv updated 2009/12/01 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
We prove an energy identity for anti-self-dual connections on the product C×Σof the complex plane and a Riemann surface. The energy is a multiple of a basic constant that is determined from the values of a corresponding Chern-Simons functional on flat connections and its ambiguity under gauge transformations. For SU(2)-bundles this identity supports the conjecture that the finite energy anti-self-dual instantons correspond to holomorphic bundles over CP1×Σ. Such anti-self-dual instantons on SU(n)- and SO(3)-bundles arise in particular as bubbles in adiabatic limits occurring in the context of mirror symmetry and the Atiyah-Floer conjecture. Our identity proves a quantization of the energy of these bubbles that simplifies and strengthens the involved analysis.