Energy identity for anti-self-dual instantons on C\times\Sigma
摘要
We prove an energy identity for anti-self-dual connections on the product C\times\Sigma of 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\times\Sigma. 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.
引用
@article{arxiv.math/0503341,
title = {Energy identity for anti-self-dual instantons on C\times\Sigma},
author = {Katrin Wehrheim},
journal= {arXiv preprint arXiv:math/0503341},
year = {2007}
}
备注
6 pages, short version of an earlier note on my homepage