Geometric construction of new Yang-Mills instantons over Taub-NUT space

TL;DR

This paper constructs a new one-parameter family of Yang-Mills instantons on Taub-NUT space, extending known solutions and employing a method inspired by flat space instanton constructions, with implications for symmetric ansatz solutions.

Contribution

It introduces a novel family of Taub-NUT instantons using a harmonic function approach and symmetry projections, expanding the set of known solutions in this geometric context.

Findings

Constructed a one-parameter family of instantons on Taub-NUT space.

Connected the solutions to known instantons at boundary points.

Provided solutions with full U(2) symmetry.

Abstract

In this paper we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L^2 harmonic 2-form, while at an inner point we recover the Pope-Yuille instanton constructed as a projection of the Levi-Civita connection onto the positive su(2) subalgebra of the Lie algebra so(4). Our method imitates the Jackiw-Nohl-Rebbi construction originally designed for flat R^4. That is we find a one-parameter family of harmonic functions on the Taub-NUT space with a point singularity, rescale the metric and project the obtained Levi-Civita connection onto the other negative su(2) subalgebra of so(4). Our solutions will possess the full U(2) symmetry, and thus provide more solutions to the recently proposed U(2) symmetric ansatz of Kim and Yoon.