Abstract
Explicit construction of the basic SU(2) anti-instantons over the multi-Taub–NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfy the so-called weak holonomy condition at infinity with respect to the trivial flat connection and decay rapidly. The resulting unit energy anti-instantons have trivial holonomy at infinity.
We also fully describe their unframed moduli space and find that it is a five dimensional space admitting a singular disk-fibration over \({\mathbb{R}^3}\) .
On the way, we work out in detail the twistor space of the multi-Taub–NUT geometry together with its real structure and transform our anti-instantons into holomorphic vector bundles over the twistor space. In this picture we are able to demonstrate that our construction is complete in the sense that we have constructed a full connected component of the moduli space of solutions of the above type.
We also prove that anti-instantons with arbitrary high integer energy exist on the multi-Taub–NUT space.
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Communicated by N.A. Nekrasov
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Etesi, G., Szabó, S. Harmonic Functions and Instanton Moduli Spaces on the Multi-Taub–NUT Space. Commun. Math. Phys. 301, 175–214 (2011). https://doi.org/10.1007/s00220-010-1146-0
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DOI: https://doi.org/10.1007/s00220-010-1146-0