Cancellation of UV divergences in ghost-free infinite derivative gravity

TL;DR

IDG introduces non-local, covariant form factors in a quadratic-curvature gravity action to achieve ghost-free UV behavior while preserving a GR-like spectrum. The authors perform a heat-kernel-based one-loop analysis to obtain explicit logarithmic divergences, expressed through coefficients multiplying $R^2$, $C^2$, and $E_{GB}$, for both monomial and general analytic form factors, and identify conditions under which these divergences can cancel. Imposing a ghost-free constraint and a sufficiently fast UV growth leads to a unique parameter choice that cancels the dangerous divergences, leaving a topological Euler term; they also discuss renormalization of boundary terms and the implications for UV finiteness. The work demonstrates a concrete route toward UV-finite, ghost-free gravity at one loop within a controlled class of non-local theories and clarifies the role of form-factor asymptotics in determining the beta functions and divergences.

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.