# Quadratic gravity in first order formalism

## TL;DR

This paper explores a quadratic curvature gravity theory in first order formalism, highlighting its potential for unitarity and renormalizability, and analyzing interactions and symmetry breaking mechanisms.

## Contribution

It develops the most general quadratic curvature gravity action in first order formalism, examining its properties and the role of Weyl invariance and matter coupling.

## Key findings

- The theory is in a conformal invariant phase without Einstein-Hilbert term.
- Interactions are mainly mediated by the three-index connection field.
- Quantum corrections can generate the Einstein-Hilbert term when Weyl invariance is broken.

## 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 $\tfrac{1}{p^2}$. Calculations are somewhat involved when all monomials are considered, but we have intended to laid down the general case. The interaction between external sources is analyzed; this interaction is conveyed mainly by the three-index connection field. The theory as it stands, is in the 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 by quantum corrections.