Large N algebras and generalized entropy

Venkatesa Chandrasekaran, Geoff Penington, Edward Witten

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number9
JournalJournal of High Energy Physics
Volume2023
Issue number4
DOIs
StatePublished - Apr 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Keywords

  • AdS-CFT Correspondence
  • Black Holes

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