Applications of the Ashtekar gravity to four dimensional hyperkähler geometry and Yang-Mills Instantons

Details Applications of the Ashtekar gravity to four dimensional hyperkähler geometry and Yang-Mills Instantons Applications of the Ashtekar gravity to four dimensional hyperkähler geometry and Yang-Mills Instantons

1996-10-10

arxiv.org/abs/hep-th/9610069v2

J.Math.Phys. 38 (1997) 5833-5839

Physics

High Energy Physics

High Energy Physics - Theory

9pages, Figures are not included

Scientific paper

10.1063/1.532169

The Ashtekar-Mason-Newman equations are used to construct the hyperk\"ahler metrics on four dimensional manifolds. These equations are closely related to anti self-dual Yang-Mills equations of the infinite dimensional gauge Lie algebras of all volume preserving vector fields. Several examples of hyperk\"ahler metrics are presented through the reductions of anti self-dual connections. For any gauge group anti self-dual connections on hyperk\"ahler manifolds are constructed using the solutions of both Nahm and Laplace equations.

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