Linear gravity from conformal symmetry

Abstract

We perform a unified systematic analysis of d + 1 dimensional, spin representations of the isometry algebra of the maximally symmetric spacetimes AdSd+1, and dSd+1. This allows us to explicitly construct the effective low-energy bulk equations of motion obeyed by linear fields, as the eigenvalue equation for the quadratic Casimir differential operator. We show that the bulk description of a conformal family is given by the Fierz–Pauli system of equations. For this is a massive gravity theory, while for conserved currents we obtain Einstein gravity and covariant gauge fixing conditions. This analysis provides a direct algebraic derivation of the familiar AdS holographic dictionary at low energies, with analogous results for Minkowski and de Sitter spacetimes.