Universality of Long-Distance AdS Physics from the CFT Bootstrap

Abstract

We begin by explicating a recent proof of the cluster decomposition principle in AdS_{d+1} from the CFT_d bootstrap in d > 2. The CFT argument also computes the leading interactions between distant objects in AdS, and we confirm the universal agreement between the CFT bootstrap and AdS gravity in the semi-classical limit. We proceed to study the generalization to 2d CFTs, which requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit. We compute these blocks in a semiclassical, large central charge approximation, and use them to prove a suitably modified theorem. In particular, from the 2d bootstrap we prove the existence of large spin operators with fixed 'anomalous dimensions' indicative of the presence of deficit angles in AdS_3. As we approach the threshold for the BTZ black hole, interpreted as a CFT scaling dimension, the twist spectrum of large spin operators becomes dense. Due to the exchange of the Virasoro identity block, primary states above the BTZ threshold mimic a thermal background for light operators. We derive the BTZ quasi-normal modes, and we use the bootstrap equation to prove that the twist spectrum is dense. Corrections to thermality could be obtained from a more refined computation of the Virasoro conformal blocks.

34+31 pages, references added, typo in higher-dimensional energy shift corrected, discussion of coefficient density bounds expanded

References in corpus (6)

• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Bounds on 4D Conformal and Superconformal Field Theories
• Comments on operators with large spin
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions

Cited by in corpus (266)

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• Out-of-Time-Order correlators in driven conformal field theories
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• Covariant odd entanglement entropy in AdS${}_3$/CFT${}_2$
• Holographic Local Operator Quenches in BCFTs
• Entanglement Suppression Due to Black Hole Scattering
• Light cone OPE in a CFT with lowest twist scalar primary
• Holographic Reflected Entropy: Islands and Defect Phases
• Differential equations for classical Virasoro blocks with heavy and light operators
• Subsystem fidelity in two-dimensional conformal field theories
• Towards $W_3$ classical blocks with semi-degenerate operators