Massive Higher Derivative Gravity in D-dimensional Anti-de Sitter Spacetimes

TL;DR

This paper analyzes a general class of higher derivative gravity theories in D-dimensional Anti-de Sitter space, deriving propagators, scattering amplitudes, and Newtonian potentials, and highlights the unique unitarity of 3D New Massive Gravity.

Contribution

It provides a comprehensive calculation of propagators and scattering amplitudes in higher derivative gravity theories in AdS space, and identifies the special status of 3D New Massive Gravity.

Findings

Derived the propagator and scattering amplitude in D-dimensional AdS.

Calculated Newtonian potentials for various limits.

Established the unitarity and Newtonian limit equivalence of 3D New Massive Gravity.

Abstract

We find the propagator and calculate the tree level scattering amplitude between two covariantly conserved sources in an Anti-de Sitter background for the most general D-dimensional quadratic, four-derivative, gravity with a Pauli-Fierz mass. We also calculate the Newtonian potential for various limits of the theory in flat space. We show how the recently introduced three dimensional New Massive Gravity is uniquely singled out among higher derivative models as a (tree level) unitary model and that its Newtonian limit is equivalent to that of the usual massive gravity in flat space.