A MacDowell–Mansouri-type formulation for conformally flat Einstein manifolds

Abstract

We study a pure connection formulation plus algebraic constraints in four spacetime dimensions where the gauge group [Formula: see text]. We show that the action has, as particular cases, the MacDowell–Mansouri and the Stelle–West formulations for gravity. Also, under adequate specification of the constraint terms, we obtain a subset of Einstein manifolds that are torsionless conformally flat manifolds.