Instantons on gravitons (Q639383)

The paper proposes a general construction for generic Yang-Mills instantons on a class of 4-dimensional instantons called ALF spaces (these are characterized by the volume of a ball of radius \(r\) growing asymptotically as \(r^3\)). The construction uses the notion of bow which is a generalization of the notion of quiver that was used for an analogous construction on ALE spaces (characterized by \(r^4\) volume growth) by \textit{P. B. Kronheimer} and \textit{H. Nakajima} [Math. Ann. 288, No.2, 263--307 (1990; Zbl 0694.53025)] and appeared already in the ADHM construction of all instanton configurations on flat \(\mathbb R^4\) [\textit{M. F. Atiyah, V. G. Drinfeld, N. J. Hitchin} and \textit{Yu. L. Manin}, Phys. Lett. A 65, No.~3, 185--187 (1978; Zbl 0424.14004)]. ALF spaces are realized as moduli spaces of certain bow representations. Bow data are, up to gauge equivalence, in one-to-one correspondence with Yang-Mills instantons. The correspondence is provided by the Nahm transform, which is shown to be an isomorphism of complex varieties in any of their complex structures.