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 $\Sigma$ and the auxiliary matrix field $\psi$ is { \it 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.
Categories: hep-th