Super-renormalizable & Finite Gravitational Theories

TL;DR

This paper introduces a class of non-polynomial higher derivative gravity theories that are super-renormalizable and potentially finite in any dimension, providing a promising approach toward consistent quantum gravity.

Contribution

It presents a novel class of non-polynomial gravity theories that are unitary, super-renormalizable, and can be made completely finite in four dimensions and possibly higher.

Findings

Theories are unitary and ghost-free.

At most one-loop divergences survive.

Explicit proof of finiteness in D=4 with all beta functions vanishing.

Abstract

We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta functions vanish even at one-loop. These results can be easily extended in extra dimensions and it is likely that the higher dimensional theory can be made finite too. Therefore we have the possibility for "finite quantum gravity" in any dimension.