Built on

P. Saad, S. H. Shenker and D. Stanford, JT gravity as a matrix integral , 1903.11115
Original
1903
Earlier work this paper cites.
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox , 1905.08255
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole , 1905.08762
Original
1905
Earlier work this paper cites.
R. Bousso, V. Chandrasekaran and A. Shahbazi-Moghaddam, From black hole entropy to energy-minimizing states in QFT , Phys. Rev. D 101
Original
1906
Earlier work this paper cites.
X. Dong and D. Marolf, One-loop universality of holographic codes , JHEP 03
Original
1910
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior , JHEP 03
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation , JHEP 05
Original
1911
Earlier work this paper cites.
A. R. Brown, H. Gharibyan, G. Penington and L. Susskind, The Python’s Lunch: geometric obstructions to decoding Hawking radiation , JHEP 08
Original
1912
Earlier work this paper cites.
I. Gelfand and M. Naimark, On the imbedding of normed rings into the ring of operators in hilbert space , Matematiceskij sbornik 54
1943
Earlier work this paper cites.
I. E. Segal, Irreducible representations of operator algebras , Bulletin of the American Mathematical Society 53
1947
Earlier work this paper cites.
H. Borchers, Über die vollständigkeit lorentzinvarianter felder in einer zeitartigen röhre , Il Nuovo Cimento (1955-1965) 19
1961
Earlier work this paper cites.
H. Araki, A generalization of borchers theorem , Helvetica Physica Acta (Switzerland) 36
1963
Earlier work this paper cites.
J. D. Bekenstein, Black Holes and Entropy , Phys. Rev. D7
1973
Earlier work this paper cites.
M. Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III , Acta Mathematica 131
1973
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity , Phys. Rev. D 15
1977
Earlier work this paper cites.
D. N. Page, Information in black hole radiation , Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
D. N. Page, Average entropy of a subsystem , Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem , Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
S. Carlip and C. Teitelboim, Aspects of black hole quantum mechanics and thermodynamics in (2+1)-dimensions , Phys. Rev. D 51
1995
Earlier work this paper cites.
L. Barnett, Free product von neumann algebras of type iii , Proceedings of the American Mathematical Society 123
1995
Earlier work this paper cites.
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy , Phys. Lett. B 379
1996
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory , Phys. Lett. B 428
1998
Earlier work this paper cites.
E. Witten, Anti-de Sitter space and holography , Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.

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J. M. Maldacena, The Large N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
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Then

A. Almheiri, X. Dong and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT , JHEP 04
Original
2015
Later among the works it cites.
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Original
2016
Later among the works it cites.
D. Harlow, Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture , JHEP 01
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J. Maldacena and D. Stanford, Comments on the sachdev-ye-kitaev model , Phys. Rev. D 94

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2022

Large N algebras and generalized entropy

Chandrasekaran, Venkatesa, Penington, Geoff, Witten, Edward

Understand

We construct a Type II$_\infty$ 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 $G \to 0$ 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.

Built on

P. Saad, S. H. Shenker and D. Stanford, JT gravity as a matrix integral , 1903.11115
Original
1903
Earlier work this paper cites.
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox , 1905.08255
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole , 1905.08762
Original
1905
Earlier work this paper cites.
R. Bousso, V. Chandrasekaran and A. Shahbazi-Moghaddam, From black hole entropy to energy-minimizing states in QFT , Phys. Rev. D 101
Original
1906
Earlier work this paper cites.
X. Dong and D. Marolf, One-loop universality of holographic codes , JHEP 03
Original
1910
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior , JHEP 03
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation , JHEP 05
Original
1911
Earlier work this paper cites.
A. R. Brown, H. Gharibyan, G. Penington and L. Susskind, The Python’s Lunch: geometric obstructions to decoding Hawking radiation , JHEP 08
Original
1912
Earlier work this paper cites.
I. Gelfand and M. Naimark, On the imbedding of normed rings into the ring of operators in hilbert space , Matematiceskij sbornik 54
1943
Earlier work this paper cites.
I. E. Segal, Irreducible representations of operator algebras , Bulletin of the American Mathematical Society 53
1947
Earlier work this paper cites.
H. Borchers, Über die vollständigkeit lorentzinvarianter felder in einer zeitartigen röhre , Il Nuovo Cimento (1955-1965) 19
1961
Earlier work this paper cites.
H. Araki, A generalization of borchers theorem , Helvetica Physica Acta (Switzerland) 36
1963
Earlier work this paper cites.
J. D. Bekenstein, Black Holes and Entropy , Phys. Rev. D7
1973
Earlier work this paper cites.
M. Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III , Acta Mathematica 131
1973
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity , Phys. Rev. D 15
1977
Earlier work this paper cites.
D. N. Page, Information in black hole radiation , Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
D. N. Page, Average entropy of a subsystem , Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
M. Banados, C. Teitelboim and J. Zanelli, Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem , Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
S. Carlip and C. Teitelboim, Aspects of black hole quantum mechanics and thermodynamics in (2+1)-dimensions , Phys. Rev. D 51
1995
Earlier work this paper cites.
L. Barnett, Free product von neumann algebras of type iii , Proceedings of the American Mathematical Society 123
1995
Earlier work this paper cites.
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy , Phys. Lett. B 379
1996
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory , Phys. Lett. B 428
1998
Earlier work this paper cites.
E. Witten, Anti-de Sitter space and holography , Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.

Similar

J. M. Maldacena, The Large N limit of superconformal field theories and supergravity , Int. J. Theor. Phys. 38
1999
Cited alongside, same era.
S. Das, P. Majumdar and R. K. Bhaduri, General logarithmic corrections to black hole entropy , Class. Quant. Grav. 19
2002
Cited alongside, same era.
J. M. Maldacena, Eternal black holes in anti-de Sitter , JHEP 04
2003
Cited alongside, same era.
J. M. Maldacena and L. Maoz, Wormholes in AdS , JHEP 02
2004
Cited alongside, same era.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT , Phys. Rev. Lett. 96
2006
Cited alongside, same era.
A. Hamilton, D. N. Kabat, G. Lifschytz and D. A. Lowe, Holographic representation of local bulk operators , Phys. Rev. D 74