AdS/CFT is the duality between quantum gravity on anti-de Sitter (AdS) spacetime and conformal field theory (CFT) on the AdS boundary. Since the CFT is unitary, the dual quantum gravity on AdS should also be unitary, and thus should not have the information paradox at all. However, what is truly important to understand is rather how and why the information paradox can be resolved in quantum gravity, and AdS/CFT plays the key role in such direction as it offers a controlled calculable setup. Such studies would lead us to a deeper understanding of the quantum structure of black holes. The recent remarkable progress in this direction is the discovery of the necessity of including Euclidean wormholes into the gravitational path integral, which renders the entropy of the Hawking radiation unitary. This result stems from the two key ingredients in AdS/CFT, the Ryu-Takayanagi formula, and the entanglement wedge reconstruction. This chapter introduces the fundamentals of AdS/CFT, the Ryu-Takayanagi formula, and the entanglement wedge reconstruction. We explain why we need an external reservoir to pose the information paradox in AdS/CFT, and why the inclusion of the Euclidean wormholes to the gravitational path-integral renders the radiation entropy unitary. We also explain why the Euclidean wormholes are tied to the ensemble average interpretation, which introduces new problems, such as the factorization problem and fluctuations in the averaged quantities.

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Unitary Evaporation and AdS/CFT

  • Masamichi Miyaji

摘要

AdS/CFT is the duality between quantum gravity on anti-de Sitter (AdS) spacetime and conformal field theory (CFT) on the AdS boundary. Since the CFT is unitary, the dual quantum gravity on AdS should also be unitary, and thus should not have the information paradox at all. However, what is truly important to understand is rather how and why the information paradox can be resolved in quantum gravity, and AdS/CFT plays the key role in such direction as it offers a controlled calculable setup. Such studies would lead us to a deeper understanding of the quantum structure of black holes. The recent remarkable progress in this direction is the discovery of the necessity of including Euclidean wormholes into the gravitational path integral, which renders the entropy of the Hawking radiation unitary. This result stems from the two key ingredients in AdS/CFT, the Ryu-Takayanagi formula, and the entanglement wedge reconstruction. This chapter introduces the fundamentals of AdS/CFT, the Ryu-Takayanagi formula, and the entanglement wedge reconstruction. We explain why we need an external reservoir to pose the information paradox in AdS/CFT, and why the inclusion of the Euclidean wormholes to the gravitational path-integral renders the radiation entropy unitary. We also explain why the Euclidean wormholes are tied to the ensemble average interpretation, which introduces new problems, such as the factorization problem and fluctuations in the averaged quantities.