Geometric interpretation of Schwarzschild instantons

JOURNAL OF GEOMETRY AND PHYSICS

卷:37

Article

Etesi, G ; Hausel, T

关键词: L-2 harmonic forms;    Euclidean Schwarzchild manifold;    dyons;   

DOI  :  10.1016/S0393-0440(00)00040-1

来源: Elsevier

【 摘 要 】

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 And 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. (C) 2001 Elsevier Science B.V. All rights reserved. MSC: Primary: 58A14; Secondary: 81T13.

【 授权许可】

Free