Physical content of Quadratic Gravity

TL;DR

This paper analyzes the physical role of the connection in quadratic gravity within the first order formalism, performing a detailed spin analysis and exploring implications for consistent truncations of the theory.

Contribution

It provides a complete spin analysis of the torsionless connection in quadratic gravity and discusses the properties of potential consistent truncations.

Findings

Detailed spin characterization of the connection

Insights into the physical interpretation of the connection

Discussion of conditions for consistent truncations

Abstract

We have recently undergone an analysis of gravitational theories as defined in first order formalism, where the metric and the connection are treated as independent fields. The physical meaning of the connection field has historically been somewhat elusive. In this paper, a complete spin analysis of the torsionless connection field is performed, and its consequences are explored. The main properties of a hypothetical consistent truncation of the theory are discussed as well.