Kerr-Schild perturbations in higher derivative gravity theories in $D$ dimensions

TL;DR

The paper develops a framework to study ghost-free infinite derivative gravity (IDG) in D dimensions via Kerr-Schild perturbations on AdS backgrounds. By focusing on AdS-plane-wave Kerr-Schild metrics, it reduces the complicated IDG field equations to linearized equations for transverse-traceless spin-2 perturbations and derives conditions on the nonlocal form factors that ensure unitarity. It shows that the nonlocal operator must be an exponential of an entire function to avoid ghosts, providing explicit examples with UV-exponential suppression and a massless graviton pole. The approach yields a tractable route to construct explicit D-dimensional form factors and demonstrates that only the massless graviton propagates with improved high-energy behavior. This has implications for constructing consistent, nonlocal gravity theories in higher dimensions with controlled perturbative stability.

Abstract

We study Kerr-Schild perturbations of a ghost-free, generic non-local gravity theory constructed from an infinite series of higher derivative terms in $D$ dimensions. The infinite series of higher derivative terms are encoded by form factors, the forms of which can be restricted by requiring that the action remains perturbatively free of ghosts and tachyons around maximally symmetric backgrounds for transverse traceless fluctuations. To demonstrate this, we obtain field equations for AdS plane wave metric in Kerr-Schild form, which yield linearized field equations for transverse-traceless spin-$2$ field. Using unitarity and consistency requirements, we obtain, as an example, the explicit derivation of non-local form factors in $D$ dimensions.