A candidate for an UV completion: quadratic gravity in first order formalism (1710.01764v1)

Abstract: We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than $\tfrac{1}{p^2}$. The UV regime is in a conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated.