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A MacDowell-Mansouri type formulation for Einstein manifolds (2304.05606v1)
Published 12 Apr 2023 in hep-th
Abstract: We study a pure connection formulation plus algebraic constraints in four spacetime dimensions where the gauge group $G \supset SO(1, 3)$. 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 Einstein manifolds, i.e., torsionless conformally flat manifolds.