Non-perturbative spectrum of non-local gravity

TL;DR

This paper analyzes the non-perturbative degrees of freedom in weakly non-local gravity theories, revealing a finite set of eight degrees of freedom in four dimensions, contrasting with the infinite derivatives suggested by the action.

Contribution

It proves that non-perturbatively, non-local gravity has eight degrees of freedom in four dimensions, and introduces a criterion to select the form factor almost uniquely.

Findings

Non-perturbative degrees of freedom are eight in four dimensions.

Six degrees of freedom do not propagate on Minkowski spacetime.

A criterion for selecting the form factor is proposed.

Abstract

We investigate the non-perturbative degrees of freedom of a class of weakly non-local gravitational theories that have been proposed as an ultraviolet completion of general relativity. At the perturbative level, it is known that the degrees of freedom of non-local gravity are the same of the Einstein--Hilbert theory around any maximally symmetric spacetime. We prove that, at the non-perturbative level, the degrees of freedom are actually eight in four dimensions, contrary to what one might guess on the basis of the "infinite number of derivatives" present in the action. It is shown that six of these degrees of freedom do not propagate on Minkowski spacetime, but they might play a role at large scales on curved backgrounds. We also propose a criterion to select the form factor almost uniquely.