General relativity without the metric

A new class of generally covariant gauge theories is introduced. The only field in addition to the gauge connection is a scalar-density Lagrange multiplier. For the group SO(3,C) [SO(3,R)] in four dimensions and particular coupling constants, the theory is equivalent to complex [Euclidean] general relativity, modulo an important degeneracy. The spacetime metric is constructed from the curvature in a solution. A canonical analysis leads directly to Ashtekar's Hamiltonian formalism. The general solution to the four diffeomorphism constraints in the nondegenerate case is given.