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Volume-preserving diffeomorphisms in integrable deformations of selfdual gravity

Kanehisa Takasaki
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Abstract

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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Kanehisa Takasaki. 1992-03-12. Volume-preserving diffeomorphisms in integrable deformations of selfdual gravity. https://doi.org/10.1016/0370-2693(92)91450-n

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