Geometric interpretation of Schwarzschild instantons

✍ Scribed by Gábor Etesi; Tamás Hausel

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 80 KB
• Volume: 37
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(00)00040-1

✦ Synopsis

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.