Towards a path integral for the pure-spin connection formulation of gravity

TL;DR

This paper proposes a path-integral formulation for pure-spin-connection gravity based on a two-form approach, revealing a non-polynomial effective action and suggesting a diagrammatic evaluation method.

Contribution

It introduces a novel path-integral approach for pure-spin-connection gravity using a two-form formulation, highlighting the non-polynomial nature of the effective action.

Findings

Effective action for spin-connection is non-polynomial.

Path-integral formulation based on two-form approach.

Proposed diagrammatic evaluation method.

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 $\Sigma$ 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.