SELF-DUAL GRAVITY AND THE CHIRAL MODEL

The self-dual Einstein equation (SDE) is shown to be equivalent to the two dimensional chiral model, with gauge group chosen as the group of area preserving diffeomorphisms of a two dimensional surface. The app roach given here leads to an analog of the Plebanski equations for gen eral self-dual metrics, and to a natural Hamiltonian formulation of th e SDE, namely that of the chiral model.