Super-renormalizable and finite gravitational theories

Leonardo Modesto,Lesław Rachwał

doi:10.1016/j.nuclphysb.2014.10.015

Leonardo Modesto, Lesław Rachwał

Open Access

https://doi.org/10.1016/j.nuclphysb.2014.10.015

Copy DOI

Journal: Nuclear Physics, Section B	Publication Date: Oct 16, 2014
Citations: 203	License type: cc-by

Affiliation: Fudan University

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.

Highlights

Quantum abelian and non-abelian gauge theories as the most complete embodiment of particle physics are all compatible with two guiding principles: “renormalizability” and “perturbative theory” in the quantum field theory framework
This is the achievement of a consistent quantum field theory for all but one fundamental interactions
The two conditions on the parameters s1 and s2 among m + 2 parameters of the theory in the quartic in curvature sector make the theory of quantum gravity finite

Summary

Introduction

Quantum abelian and non-abelian gauge theories as the most complete embodiment of particle physics are all compatible with two guiding principles: “renormalizability” and “perturbative theory” in the quantum field theory framework. This is the achievement of a consistent quantum field theory for all but one fundamental interactions. We here use the terminology “kinetic part” for operators linear or quadratic in the gravitational curvature, and “potential” for a finite sum of all other local operators in the action It is clear from the discussion above that we regard as crucial to find a “new theory of gravity”, which is unitary and renormalizable or even finite at quantum level. With symbol R we generally denote one of the above curvature tensors

Modern Gravity

Strict analysis of quantum divergences

Quantum modern gravity

Conclusions & Remarks