Instantons on multi-Taub-NUT spaces. I: Asymptotic form and index theorem
In the paper under review the authors study the finite action of an anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. Under a technical assumption the curvature and the harmonic spinor decay rates are established and the index of the associated Dirac operator is computed. The authors claim that this paper is the first in a series of papers proving the completeness of the bow construction of instantons on multi-Taub-NUT spaces and exploring it in detail. The analysis provided within the paper assumes a generic asymptotic holonomy condition: there exists a ray in the base \(\mathbb{R}^3\) such that the holonomy of the instanton connection around every circle fiber over that ray is generic (i.e., belongs to a common compact subset of the regular \(\mathrm{U} (n)\) adjoint orbit). More precisely, the authors assume that the eigenvalues of the holonomy over some ray in the base \(\mathbb{R}^3\) are distinct with the distance between distinct eigenvalues bounded below by a positive constant.
curvature and harmonic spinor decay rates
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