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

In this Letter 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 L2 harmonic 2-form, while at an inner point we recover the Pope–Yuille instanton constructed as a projection of the Levi-Civitá connection onto the positive su(2)+⊂so(4) subalgebra. Our method imitates the Jackiw–Nohl–Rebbi construction originally designed for flat R4. 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-Civitá connection onto the other negative su(2)−⊂so(4) part. 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.