Universally Finite Gravitational & Gauge Theories

TL;DR

This paper introduces a class of weakly non-local higher derivative gravitational and gauge theories that are universally consistent, unitary, and renormalizable across all spacetime dimensions, potentially leading to a finite standard model of particle physics.

Contribution

It presents new weakly non-local higher derivative theories that are renormalizable and finite in any dimension, extending the scope of quantum consistent theories of gravity and gauge interactions.

Findings

Theories are unitary and ghost-free.

They are perturbatively renormalizable in any dimension.

Extensions can be super-renormalizable or finite, including gravity coupled to matter.

Abstract

It is well known that standard gauge theories are renormalizable in D=4 while Einstein gravity is renormalizable in D=2. This is where the research in the field of two derivatives theories is currently standing. We hereby present a class of weakly non-local higher derivative gravitational and gauge theories universally consistent at quantum level in any spacetime dimension. These theories are unitary (ghost-free) and perturbatively renormalizable. Moreover, we can always find a simple extension of these theories that is super-renormalizable or finite at quantum level in even and odd spacetime dimensions. Finally, we propose a super-renormalizable or finite theory for gravity coupled to matter laying the groundwork for a "finite standard model of particle physics" and/or a grand unified theory of all fundamental interactions.