Self-dual 2-forms and gravity

A Palatini-type formulation of gravity coupled to matter and supergravity is given, in which the gravitational variables are a trio of self-dual 2-forms and an SL(2,C) connection. The action is polynomial in all the fields. This framework is shown to be the natural covariantization of Ashtekar's canonical formalism (1988), and is used to find the general vacuum solution of the four initial value constraints associated with spacetime diffeomorphisms in that formalism.