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A<sc>bstract</sc> We construct a Type II∞von Neumann algebra that describes the largeNphysics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative 1/Ncorrections. 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 theG →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.
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The power of Lorentzian wormholes
A<sc>bstract</sc> As shown by Louko and Sorkin in 1995, topology change in Lorentzian signature involves spacetimes with singular points, which they called crotches. We modify their construction to obtain Lorentzian semiclassical wormholes in asymptotically AdS. These solutions are obtained by inserting crotches on known saddles, like the double-cone or multiple copies of the Lorentzian black hole. The crotches implement swap-identifications, and are classically located near an extremal surface. The resulting Lorentzian wormholes have an instanton action equal to their area, which is responsible for topological suppression in any number of dimensions. We conjecture that including such Lorentzian wormhole spacetimes is equivalent to path integrating over all mostly Euclidean smooth spacetimes. We present evidence for this by reproducing semiclassical features of the genus expansion of the spectral form factor, and of a late-time two point function, by summing over the moduli space of Lorentzian wormholes. As a final piece of evidence, we discuss the Lorentzian version of West-Coast replica wormholes.
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- PAR ID:
- 10477576
- Publisher / Repository:
- Springer-Verlag
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2023
- Issue:
- 10
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP10(2023)005
