Symmetries, Currents and Conservation Laws of Self-Dual Gravity

TL;DR

This paper uncovers an infinite-dimensional algebra of hidden symmetries in self-dual gravity, including affine extensions of Lorentz rotations and diffeomorphisms, with implications for string theory.

Contribution

It introduces a new symmetry algebra combining Kac-Moody and Virasoro-like generators for self-dual gravity equations.

Findings

Identifies an infinite-dimensional symmetry algebra for self-dual gravity.

Includes new hidden symmetries extending Lorentz rotations.

Shows how these symmetries map solutions to solutions.

Abstract

We describe an infinite-dimensional algebra of hidden symmetries for the self-dual gravity equations. Besides the known diffeomorphism-type symmetries (affine extension of w(infinity) algebra), this algebra contains new hidden symmetries, which are an affine extension of the Lorentz rotations. The full symmetry algebra has both Kac-Moody and Virasoro-like generators, whose exponentiation maps solutions of the field equations to other solutions. Relations to problems of string theories are briefly discussed.