2022/09/21 by Venkatesa Chandrasekaran, Geoff Penington, Edward Witten · 1 voice
Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #Entropy (arrow of time) #Geometry #Mathematical physics #Noncommutative and Quantum Gravity Theories #Operator product expansion #Physics #Quantum #Quantum entanglement #Quantum gravity #Quantum mechanics #Semiclassical physics #Theoretical physics #Von Neumann entropy #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep04(2023)009
arxiv published 2022/09/21 · arxiv updated 2022/09/21 · openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A bstract We construct a Type II ∞ von Neumann algebra that describes the large N physics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative 1 /N corrections. Using only the extrapolate dictionary, we show that the entropy of semiclassical states on this algebra is holographically dual to the generalized entropy of the black hole bifurcation surface. From a boundary perspective, this constitutes a derivation of a special case of the QES prescription without any use of Euclidean gravity or replicas; from a purely bulk perspective, it is a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy of an explicit algebra in the G → 0 limit of Lorentzian effective field theory quantum gravity. In a limit where a black hole is first allowed to equilibrate and then is later potentially re-excited, we show that the generalized second law is a direct consequence of the monotonicity of the entropy of algebras under trace-preserving inclusions. Finally, by considering excitations that are separated by more than a scrambling time we construct a “free product” von Neumann algebra that describes the semiclassical physics of long wormholes supported by shocks. We compute Rényi entropies for this algebra and show that they are equal to a sum over saddles associated to quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles associated to “bulge” quantum extremal surfaces contribute with a negative sign.