Cancellation of UV divergences in ghost-free infinite derivative gravity

TL;DR

This paper investigates how specific non-local form factors in ghost-free infinite derivative gravity can cancel ultraviolet divergences at one-loop, potentially leading to a finite quantum gravity theory.

Contribution

It derives conditions on form factors that ensure the complete cancellation of one-loop divergences in a broad class of ghost-free, non-local gravity models.

Findings

Identifies form factors that eliminate one-loop divergences in the ultraviolet limit.

Provides explicit expressions for beta functions of couplings in these models.

Shows that divergences can be canceled beyond the Tomboulis class of form factors.

Abstract

We consider the most general covariant gravity action up to terms that are quadratic in curvature. These can be endowed with generic form factors, which are functions of the d'Alembert operator. If they are chosen in a specific way as an exponent of an entire function, the theory becomes ghost-free and renormalizable at the price of non-locality. Furthermore, according to power-counting arguments, if these functions grow sufficiently fast along the real axis, divergences may only appear at the first order in loop expansion. Using the heat kernel technique, we compute the one-loop logarithmic divergences in the ultraviolet limit and determine the conditions under which they vanish completely, apart from the Gauss--Bonnet term and a surface term, both of which can be neglected on a four-dimensional manifold without a boundary. We identify form factors both within the Tomboulis class and beyond it that lead to vanishing logarithmic divergences. The general expression for the one-loop beta functions of the dimensionless couplings in quadratic gravity with asymptotically monomial form factors is given.