Harmonic functions and instanton moduli spaces on the multi-Taub--NUT space

TL;DR

This paper constructs explicit anti-instantons on multi-Taub--NUT space, describes their moduli space, and demonstrates the existence of high-energy solutions, advancing understanding of gauge fields in gravitational instanton backgrounds.

Contribution

It provides a complete construction of anti-instantons on multi-Taub--NUT space, including their moduli space and twistor space analysis, with new results on high-energy solutions.

Findings

Explicit anti-instantons constructed via conformal rescaling

Moduli space described as a five-dimensional singular disk-fibration

Existence of anti-instantons with arbitrarily high energy

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 satisfiy the so-called weak holonomy condition at infinity with respect to the trivial flat connection and decay rapidly. The resulting unital 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 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.