EXTENDED CONFORMAL-SYMMETRIES IN REAL HEAVENS

Real, self-dual, euclidean Einstein spaces (real heavens) admitting one rotational Killing symmetry are shown to posses the extended conformal symmetries - the large n limit of Zamolodchikov's Wn algebra. Explicit transformation rules corresponding to each conformal spin kε{lunate}Z are derived and they are shown to form a representation of a symmetry algebra isomorphic to sdiff+R2 - a subalgebra of locally area preserving diffeomorphisms. This relates two dimensional conformal field theory with four dimensional integrable systems and provides a systematic way to generalize the Eguchi-Hanson gravitational instanton. © 1990.