Energy identity for anti-self-dual instantons on C\timesΣ

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dc.creatorWehrheim, Katrin
dc.date2005-03-16
dc.date.accessioned2026-07-07T05:18:02Z
dc.date.available2026-07-07T05:18:02Z
dc.descriptionWe prove an energy identity for anti-self-dual connections on the product C\timesΣof 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 CP^1\timesΣ. 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.
dc.description6 pages, short version of an earlier note on my homepage
dc.identifierhttps://arxiv.org/abs/math/0503341
dc.identifierhttp://arxiv.org/abs/math/0503341
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74523
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject53C07; 57Rxx
dc.titleEnergy identity for anti-self-dual instantons on C\timesΣ
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