Linear gravity from conformal symmetry

Tuesday, 30 October, 2018

Published in: 

arXiv:1810.12923

We perform a unified systematic analysis of d+1 dimensional, spin \ell representations of the isometry algebra of the maximally symmetric spacetimes AdS_d+1, \mathbb{R}_{1,d} and dS_d+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 \ell=2 this is a massive gravity theory, while for \ell=2 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.

Author(s): 

Julian Sonner
Benjamin Withers