Towards a path integral for pure spin connection formulation of gravity

Abstract

A proposal for the path-integral of pure-spin-connection formulation of gravity is described, based on the two-form formulation of Capovilla et. al. It is shown that the resulting effective-action for the spin-connection, upon functional integration of the two-form field Σ and the auxiliary matrix field ψ is non-polynomial, even for the case of vanishing cosmological constant and absence of any matter couplings.Further, a diagramatic evaluation is proposed for the contribution of the matrix-field to the pure spin connection action.