Anti-self-dual Maxwell solutions on hyperkähler manifold and N=2 supersymmetric Ashtekar gravity

Details Anti-self-dual Maxwell solutions on hyperkähler manifold and N=2 supersymmetric Ashtekar gravity Anti-self-dual Maxwell solutions on hyperkähler manifold and N=2 supersymmetric Ashtekar gravity

1998-09-30

arxiv.org/abs/gr-qc/9809083v1

Class.Quant.Grav. 16 (1999) 1305-1312

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

10.1088/0264-9381/16/4/019

Anti-self-dual (ASD) Maxwell solutions on 4-dimensional hyperk\"ahler manifolds are constructed. The N=2 supersymmetric half-flat equations are derived in the context of the Ashtekar formulation of N=2 supergravity. These equations show that the ASD Maxwell solutions have a direct connection with the solutions of the reduced N=2 supersymmetric ASD Yang-Mills equations with a special choice of gauge group. Two examples of the Maxwell solutions are presented.

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