Linear gravity from conformal symmetry

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.

21 pages, 1 figure

References in corpus (8)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Holography from Conformal Field Theory
• Holographic representation of local bulk operators
• The boundary dual of the bulk symplectic form
• From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
• Holographic Representation of Higher Spin Gauge Fields
• Notes on $\widetilde{\mathrm{SL}}(2,\mathbb{R})$ representations
• AdS/CFT Correspondence in Operator Formalism