Volume-preserving diffeomorphisms in integrable deformations of selfdual gravity

TL;DR

This paper explores the role of volume-preserving diffeomorphisms in an integrable deformation of selfdual gravity, revealing infinite symmetries and potential links to string theory.

Contribution

It identifies the significance of volume-preserving diffeomorphisms in a specific integrable model of selfdual gravity and connects these symmetries to twistor space and string theory.

Findings

Existence of infinite symmetries extending $w_{1+ ablafty}$ in the model

Twisted volume form on twistor space underpins these symmetries

Potential connection between the model and Witten's 2D string theory

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.