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**11 - 13**of**13**### WITS-CTP-120 Entanglement Entropy of Extremal BTZ Pawe l Caputa1∗, Vishnu Jejjala1†, Hesam Soltanpanahi1,2‡

"... In this note, we use entanglement entropy as a tool to explore the universal properties of CFTs dual to extremal BTZ black holes. We demonstrate that the entanglement entropies computed in the CFTs at the boundary of the extremal BTZ and the boundary of the near-horizon limit of the extremal BTZ are ..."

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In this note, we use entanglement entropy as a tool to explore the universal properties of CFTs dual to extremal BTZ black holes. We demonstrate that the entanglement entropies computed in the CFTs at the boundary of the extremal BTZ and the boundary of the near-horizon limit of the extremal BTZ are in perfect agreement and have the form appropriate to a two-dimensional CFT with only the chiral part excited and the anti-chiral in the ground state. Furthermore, we analyze the universal limits of the entanglement entropy and recover the correct value of the thermal entropy for large entangling intervals and the first-law like relation for the small interval.

### Universality of Long-Distance AdS Physics from the CFT Bootstrap

, 2014

"... 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-clas ..."

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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 CFT2, which requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit. We compute these blocks in a semi-classical, 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 AdS3. 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 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.