Geometric Interpretation of Schwarzschild Instantons
Abstract
In this note we address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L^2 harmonic 2-forms on the space. Gibbons found a non-topological L^2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energy. We imitate his construction in the case of the Euclidean Schwarzschild manifold and find a non-topological self-dual L^2 harmonic 2-form on it. We show how this gives rise to Abelian instantons and identify them with SU(2)-instantons of Pontryagin number 2n^2 found by Charap and Duff in 1977. Using results of Dodziuk and Hitchin we also calculate the full L^2 harmonic space for the Euclidean Schwarzschild manifold.
Keywords
Cite
@article{arxiv.hep-th/0003239,
title = {Geometric Interpretation of Schwarzschild Instantons},
author = {Gabor Etesi and Tamas Hausel},
journal= {arXiv preprint arXiv:hep-th/0003239},
year = {2009}
}
Comments
Latex, 11 pages, no figures, final, published version