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

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.