Geometric Interpretation of Schwarzschild Instantons

Details Geometric Interpretation of Schwarzschild Instantons Geometric Interpretation of Schwarzschild Instantons

2000-03-27

arxiv.org/abs/hep-th/0003239v2

J.Geom.Phys. 37 (2001) 126-136

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 11 pages, no figures, final, published version

Scientific paper

10.1016/S0393-0440(00)00040-1

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.

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