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

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

2001-05-13

arxiv.org/abs/hep-th/0105118v4

Phys.Lett. B514 (2001) 189-199

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTex, no figures

Scientific paper

10.1016/S0370-2693(01)00821-8

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.

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