THE AFFINE SYMMETRY OF SELF-DUAL GRAVITY

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 gravi ty contains an infinite dimensional hidden symmetry whose generators f orm the Affine (Kac-Moody) algebra associated with the Lie algebra of area preserving diffeomorphisms. This result provides an observable al gebra and a solution generating technique for self-dual gravity. (C) 1 995 American Institute of Physics.