A candidate for an UV completion: quadratic gravity in first order formalism

TL;DR

This paper explores a quadratic curvature gravity theory in first order formalism as a potential UV-complete, unitary, and renormalizable quantum gravity model, emphasizing its conformal invariance and mechanisms for generating Einstein-Hilbert terms.

Contribution

It introduces a quadratic curvature gravity framework in first order formalism, highlighting its potential for UV completion and the role of conformal invariance in its dynamics.

Findings

The theory is potentially unitary and renormalizable.

No propagators fall faster than 1/p^2 in the UV.

Conformal invariance is key to the UV behavior and generation of Einstein-Hilbert term.

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.