Dynamical Implementation of the Constraints in Conformal Gravity

TL;DR

This paper introduces a geometric Lagrangian formulation for four-dimensional conformal gravity that dynamically enforces standard constraints, clarifying its gauge-theoretic structure and enabling extensions to higher dimensions and supersymmetry.

Contribution

It presents a first-order geometric Lagrangian for conformal gravity that dynamically implements the standard constraints within the Cartan formulation.

Findings

The Lagrangian yields the expected constraints dynamically.

The theory reduces to standard conformal gravity with quadratic curvature invariants.

Clarifies the geometric gauge theory status of conformal gravity.

Abstract

We propose a first-order geometric Lagrangian for four-dimensional conformal gravity within the Cartan formulation, which yields, dynamically, the standard constraints on the fields, expected for conformal gravity. Upon imposing the dynamical constraints, together with the request of conformal invariance of the off-shell Lagrangian, the theory reduces to the standard expression for conformal gravity, in terms of quadratic curvature invariants. Our results clarify the geometric status of conformal gravity as a gauge theory and open the way to a similar dynamical implementation of the constraints in higher dimensions and supersymmetric extensions.