Universality of long-distance AdS physics from the CFT bootstrap

• Published in: The journal of high energy physics 2014-08, Vol.2014 (8), p.1, Article 145
• Main Authors: Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T.
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2014)145

A bstract We begin by explicating a recent proof of the cluster decomposition principle in AdS ≥4 from the CFT ≥3 bootstrap. The CFT argument also computes the leading interactions between distant objects in AdS ≥4 , 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 CFT 2 , 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 d = 2 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 2 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 quasinormal 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.