Volume-preserving diffeomorphisms in integrable deformations of selfdual gravity

Details Volume-preserving diffeomorphisms in integrable deformations of selfdual gravity Volume-preserving diffeomorphisms in integrable deformations of selfdual gravity

1992-03-12

arxiv.org/abs/hep-th/9203034v1

Phys.Lett. B285 (1992) 187-190

Physics

High Energy Physics

High Energy Physics - Theory

9 pages

Scientific paper

10.1016/0370-2693(92)91450-N

A group of volume-preserving diffeomorphisms in 3D turns out to play a key role in an Einstein-Maxwell theory whose Weyl tensor is selfdual and whose Maxwell tensor has algebraically general anti-selfdual part. This model was first introduced by Flaherty and recently studied by Park as an integrable deformation of selfdual gravity. A twisted volume form on the corresponding twistor space is shown to be the origin of volume-preserving diffeomorphisms. An immediate consequence is the existence of an infinite number of symmetries as a generalization of $w_{1+\infty}$ symmetries in selfdual gravity. A possible relation to Witten's 2D string theory is pointed out.

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