Graded algebraic structure in the canonical formulation of N = 3 chiral supergravity

Abstract

We focus on N = 3 chiral supergravity (SUGRA) which is the lowest N theory involving a spin-1/2 field, and derive the Ashtekar's canonical formulation of N = 3 SUGRA starting with the chiral Lagrangian constructed by closely following the standard SUGRA. The polynomiality of constraints in terms of canonical variables and the graded algebraic structure of constraints are discussed in the canonical formulation. In particular, we show the polynomiality of the {\it rescaled} right- and left-handed SUSY constraints by a nonpolynomial factor. And also we show the graded algebraic structure of Osp(3/2) in the constraint algebra by calculating the Poisson brackets of Gauss, SU(2) gauge and right-handed SUSY constraints, although the algebra among only those three types of constraints does not closed.