THE ASHTEKAR FORMULATION FOR CANONICAL N=2 SUPERGRAVITY

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Abstract
Ashtekar’s formulation of canonical gravity is extended to N=2 supergravity. The action has a complex first-order chiral form and is invariant under two local supersymmetry transformations. Since we adopt the chiral formulation, left- and right-handed supersymmetries appear in an asymmetric way. The supersymmetry algebra is not closed on auxiliary fields, which is a peculiar result of the chiral formulation, where the right-handed supersymmetries are realized by constrained parameters. By means of the canonical formalism, simple polynomial constraints are derived and we can show that the Poisson brackets of supersymmetry currents are actually closed. This guarantees the consistency of our supersymmetry transformations, which is unclear at the level of the algebra on the fields.

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