Built on

C. R. Graham and M. J. Gursky, Chern-Gauss-Bonnet formula for singular Yamabe metrics in dimension four , 1902.01562
Original
1902
Earlier work this paper cites.
G. Anastasiou, I. J. Araya, A. Guijosa and R. Olea, Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs , JHEP 10
Original
1908
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry , 1908.10996
Original
1908
Earlier work this paper cites.
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon , 1910.11077
Original
1910
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation , 1911.12333
Original
1911
Earlier work this paper cites.
S.-S. Chern, A simple intrinsic proof of the gauss-bonnet formula for closed riemannian manifolds , Annals of Mathematics 45
1944
Earlier work this paper cites.
J. S. Dowker and J. P. Schofield, Conformal Transformations and the Effective Action in the Presence of Boundaries , J. Math. Phys. 31
1990
Earlier work this paper cites.
D. N. Page, Information in black hole radiation , Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
M. Henningson and K. Skenderis, Weyl anomaly for Wilson surfaces , JHEP 06
1999
Earlier work this paper cites.
C. R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS / CFT correspondence , Nucl. Phys. B546
1999
Earlier work this paper cites.
S. de Haro, K. Skenderis and S. N. Solodukhin, Holographic reconstruction of spacetime¶and renormalization in the ads/cft correspondence , Communications in Mathematical Physics 217
2001
Earlier work this paper cites.
M. T. Anderson, L 2 curvature and volume renormalization of the ahe metrics on 4 manifolds , Math. Res. Lett. 8
2001
Earlier work this paper cites.

Similar

G. Anastasiou, J. Moreno, R. Olea and D. Rivera-Betancour, Shape dependence of renormalized holographic entanglement entropy , 2002.06111
Original
2002
Cited alongside, same era.
I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes , JHEP 08
2005
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I. Papadimitriou and K. Skenderis, AdS / CFT correspondence and geometry , IRMA Lect. Math. Theor. Phys. 8
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Cited alongside, same era.

Then

T. Faulkner, M. Guica, T. Hartman, R. C. Myers and M. Van Raamsdonk, Gravitation from Entanglement in Holographic CFTs , JHEP 03
Original
2014
Later among the works it cites.
M. Taylor and W. Woodhead, Renormalized entanglement entropy , JHEP 08
Original
2016
Later among the works it cites.
A. R. Gover and A. Waldron, Renormalized Volume , Commun. Math. Phys. 354
Original
2017
Later among the works it cites.
C. Graham, Volume renormalization for singular Yamabe metrics , Proc. Am. Math. Soc. 145
2017
Later among the works it cites.
S. Fischetti and T. Wiseman, A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow , Class. Quant. Grav. 34
Original
2017

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2020

Renormalized entanglement entropy and curvature invariants

Taylor, Marika, Too, Linus

Understand

Renormalized entanglement entropy can be defined using the replica trick for any choice of renormalization scheme; renormalized entanglement entropy in holographic settings is expressed in terms of renormalized areas of extremal surfaces.

In this paper we show how holographic renormalized entanglement entropy can be expressed in terms of the Euler invariant of the surface and renormalized curvature invariants.
For a spherical entangling region in an odd-dimensional CFT, the renormalized entanglement entropy is proportional to the Euler invariant of the holographic entangling surface, with the coefficient of proportionality capturing the (renormalized) F quantity.
Variations of the entanglement entropy can be expressed elegantly in terms of renormalized curvature invariants, facilitating general proofs of the first law of entanglement.

Built on

C. R. Graham and M. J. Gursky, Chern-Gauss-Bonnet formula for singular Yamabe metrics in dimension four , 1902.01562
Original
1902
Earlier work this paper cites.
G. Anastasiou, I. J. Araya, A. Guijosa and R. Olea, Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs , JHEP 10
Original
1908
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry , 1908.10996
Original
1908
Earlier work this paper cites.
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon , 1910.11077
Original
1910
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation , 1911.12333
Original
1911
Earlier work this paper cites.
S.-S. Chern, A simple intrinsic proof of the gauss-bonnet formula for closed riemannian manifolds , Annals of Mathematics 45
1944
Earlier work this paper cites.
J. S. Dowker and J. P. Schofield, Conformal Transformations and the Effective Action in the Presence of Boundaries , J. Math. Phys. 31
1990
Earlier work this paper cites.
D. N. Page, Information in black hole radiation , Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
M. Henningson and K. Skenderis, Weyl anomaly for Wilson surfaces , JHEP 06
1999
Earlier work this paper cites.
C. R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS / CFT correspondence , Nucl. Phys. B546
1999
Earlier work this paper cites.
S. de Haro, K. Skenderis and S. N. Solodukhin, Holographic reconstruction of spacetime¶and renormalization in the ads/cft correspondence , Communications in Mathematical Physics 217
2001
Earlier work this paper cites.
M. T. Anderson, L 2 curvature and volume renormalization of the ahe metrics on 4 manifolds , Math. Res. Lett. 8
2001
Earlier work this paper cites.

Similar

G. Anastasiou, J. Moreno, R. Olea and D. Rivera-Betancour, Shape dependence of renormalized holographic entanglement entropy , 2002.06111
Original
2002
Cited alongside, same era.
I. Papadimitriou and K. Skenderis, Thermodynamics of asymptotically locally AdS spacetimes , JHEP 08
2005
Cited alongside, same era.
I. Papadimitriou and K. Skenderis, AdS / CFT correspondence and geometry , IRMA Lect. Math. Theor. Phys. 8
2005
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.
P. Calabrese and J. Cardy, Entanglement and correlation functions following a local quench: a conformal field theory approach , J. Stat. Mech. 0710
Original
2007
Cited alongside, same era.