Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem
  We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator.   This 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. 
Sergey A. Cherkis, Andres Larrain-Hubach, and Mark Stern
math.DG hep-th