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# Linear gravity from conformal symmetry

Sonner, Julian and Withers, Benjamin (2019) Linear gravity from conformal symmetry. Classical and Quantum Gravity, 36 (8), 1-15, [085011].

Record type: Article

## Abstract

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.

Text
paper - Accepted Manuscript

Accepted/In Press date: 6 March 2019
e-pub ahead of print date: 2 April 2019
Published date: 2 April 2019
Keywords: Holography, Gravity, Conformal Field Theory

## Identifiers

Local EPrints ID: 435831
URI: http://eprints.soton.ac.uk/id/eprint/435831
ISSN: 1361-6382
PURE UUID: 1738b9ae-6014-473a-b3fd-a115560e1979

## Catalogue record

Date deposited: 21 Nov 2019 17:30

## Contributors

Author: Julian Sonner
Author: Benjamin Withers