New variables for canonical supergravity

Ashtekar's reformulation (1987) of canonical general relativity is extended to simple supergravity in four dimensions. The key idea is to use the left-handed spin connection as a complex coordinate on the phase space. The constraints are simple polynomial functions of degree four or less when expressed in terms of the new conjugate variables. The reformulation is derived starting from a complex first-order supergravity action. The action is invariant under left- and right-handed supersymmetry transformations which are not conjugate, since the connection varies in the latter case but not in the former.