The Affine symmetry of self-dual gravity

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.

20 pages, RevTex, a few presentational changes - version to appear in J. Math. Phys

References in corpus (3)

• Self-dual gravity as a two dimensional theory and conservation laws
• Self-dual gravity and the chiral model
• Einstein's equations and the chiral model

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