Linear gravity from conformal symmetry
Linear gravity from conformal symmetry
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.
Holography, Gravity, Conformal Field Theory
1-15
Sonner, Julian
1d2008de-dbc3-4231-95e6-a3d2ec93d3c1
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
2 April 2019
Sonner, Julian
1d2008de-dbc3-4231-95e6-a3d2ec93d3c1
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
Sonner, Julian and Withers, Benjamin
(2019)
Linear gravity from conformal symmetry.
Classical and Quantum Gravity, 36 (8), , [085011].
(doi:10.1088/1361-6382/ab0d3f).
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.
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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
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Date deposited: 21 Nov 2019 17:30
Last modified: 17 Mar 2024 02:27
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Author:
Julian Sonner
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