Universality of long-distance AdS physics from the CFT bootstrap

We begin by explicating a recent proof of the cluster decomposition principle in AdS(a parts per thousand yen4) from the CFTa parts per thousand yen3 bootstrap. The CFT argument also computes the leading interactions between distant objects in AdS(a parts per thousand yen4), 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 CFT2, 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 CFT2 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.