2-DIMENSIONAL GENERAL COVARIANCE FROM 3 DIMENSIONS

A 3D generally covariant field theory having some unusual properties i s described. The theory has a degenerate 3-metric which effectively ma kes it a 2D field theory in disguise. For 2-manifolds without boundary , it has an infinite number of conserved charges that are associated w ith graphs in two dimensions and the algebra of the charges is closed. For 2-manifolds with boundary there are additional observables that h ave a Kac-Moody Poisson alegebra. It is further down that the theory i s classically integrable and the general solution of the equations of motion is given. The quantum theory is described using Dirac quantizat ion, and it is shown that there are quantum states with graphs in two dimensions.