The Affine symmetry of self-dual gravity

TL;DR

This paper reveals that self-dual gravity possesses an infinite-dimensional affine symmetry, derived from its reformulation as a principal chiral model with area-preserving diffeomorphisms, offering new tools for understanding and solving the theory.

Contribution

It demonstrates that self-dual gravity has an affine Kac-Moody symmetry, providing an observable algebra and solution-generating methods.

Findings

Identification of affine Kac-Moody symmetry in self-dual gravity

Establishment of an observable algebra for the theory

Development of a solution generating technique

Abstract

Self-dual gravity may be reformulated as the two dimensional principal chiral model with the group of area preserving diffeomorphisms as its gauge group. Using this formulation, it is shown that self-dual gravity contains an infinite dimensional hidden symmetry whose generators form the Affine (Kac-Moody) algebra associated with the Lie algebra of area preserving diffeomorphisms. This result provides an observable algebra and a solution generating technique for self-dual gravity.