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

TL;DR

This paper investigates Kerr-Schild perturbations in ghost-free non-local gravity theories with higher derivatives in arbitrary dimensions, deriving conditions for ghost-free form factors and analyzing linearized equations for transverse traceless modes.

Contribution

It provides a framework for constructing ghost-free non-local gravity actions with higher derivatives and derives explicit form factors ensuring unitarity in $D$ dimensions.

Findings

Derived linearized field equations for Kerr-Schild perturbations.

Explicitly obtained non-local form factors satisfying unitarity.

Established conditions for ghost and tachyon freedom in the theory.

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.