The Gauge Theory of the de-Sitter Group and Ashtekar Formulation

TL;DR

This paper develops a gauge-theoretic approach to de Sitter gravity by incorporating a topological invariant, leading to a quadratic Chern-Simons type action that yields the Ashtekar formulation.

Contribution

It introduces a novel gauge-theoretic framework for de Sitter gravity by adding a Pontrjagin invariant, resulting in a new action from which Ashtekar variables are derived.

Findings

Derivation of a quadratic Chern-Simons type action for de Sitter gauge theory

Connection between topological invariants and Ashtekar formulation

New insights into the gauge structure of de Sitter gravity

Abstract

By adding the Pontrjagin topological invariant to the gauge theory of the de Sitter group proposed by MacDowell and Mansouri we obtain an action quadratic in the field-strengths, of the Chern-Simons type, from which the Ashtekar formulation is derived.