Canonical formulation of N=2 supergravity in terms of the Ashtekar variable - art. no. 064020

We reconstruct Ashtekar's canonical formulation of N = 2 supergravity (SUGR A) starting from the N = 2 chiral Lagrangian derived by closely following t he method employed in the usual SUGRA. In order to obtain the full graded a lgebra of the Gauss U(1) gauge and right-handed supersymmetry (SUSY) constr aints, we extend the internal, global O(2) invariance to a local one by int roducing a cosmological constant to the chiral Lagrangian. The resultant La grangian does not contain any auxiliary fields in contrast with the two-for m SUGRA, and the SUSY transformation parameters are not constrained at all. We derive the canonical formulation of the N = 2 theory in such a manner t hat the relation with the usual SUGRA is explicit, at least at the classica l level, and show that the algebra of the Gauss U(1) gauge, and right-hande d SUSY constraints form the graded algebra, G(2)SU(2). Furthermore, we intr oduce the graded variables associated with the G(2)SU(2) algebra, and we re write the canonical constraints in a simple form in terms of these variable s. We quantize the theory in the graded-connection representation, and disc uss the solutions of quantum constraints.