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.

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

References in corpus (1)

• L^2 cohomology of hyperkähler quotients

Cited by in corpus (16)

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• Classification of 't Hooft instantons over multi-centered gravitational instantons
• New self-dual solutions of SU(2) Yang-Mills theory in Euclidean Schwarzschild space
• Harmonic Forms and Spinors on the Taub-bolt Space
• On the black hole/string transition
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• Abelian instantons over the Chen-Teo AF geometry
• Schwarzschild Instanton in Emergent Gravity