Built on

K. Osterwalder and R. Schrader, “Axioms For Euclidean Green’s Functions,” Commun. Math. Phys. 31
1973
Earlier work this paper cites.
A. Zee, “Spontaneously Generated Gravity,” Phys. Rev. D 23
1981
Earlier work this paper cites.
S. L. Adler, “Einstein Gravity as a Symmetry Breaking Effect in Quantum Field Theory,” Rev. Mod. Phys. 54
1983
Earlier work this paper cites.
H. Muratani and S. Wada, “The Divergent Parts Of Quantum Fluctuation In The Curved Space From The Adler-zee Formulae,” Phys. Rev. D 29
1984
Earlier work this paper cites.
A. Cappelli, D. Friedan and J. I. Latorre, “C theorem and spectral representation,” Nucl. Phys. B 352
1991
Earlier work this paper cites.
R. Haag, “Local quantum physics: Fields, particles, algebras,” Berlin, Germany: Springer (1992). (Texts and monographs in physics)
1992
Earlier work this paper cites.
L. Bombelli, R. K. Koul, J. Lee and R. D. Sorkin, “A Quantum Source of Entropy for Black Holes,” Phys. Rev. D 34
1993
Earlier work this paper cites.
L. Susskind and J. Uglum, “Black hole entropy in canonical quantum gravity and superstring theory,” Phys. Rev. D 50
1994
Earlier work this paper cites.
D. V. Fursaev and S. N. Solodukhin, “On one loop renormalization of black hole entropy,” Phys. Lett. B 365
Original
1995
Earlier work this paper cites.
F. Larsen and F. Wilczek, “Renormalization of black hole entropy and of the gravitational coupling constant,” Nucl. Phys. B 458
1996
Earlier work this paper cites.
L. Susskind, “The World as a hologram,” J. Math. Phys. 36
1998
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech. 0406
2004
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement and alpha entropies for a massive scalar field in two dimensions,” J. Stat. Mech. 0512
2005
Earlier work this paper cites.

Similar

H. Casini, C. D. Fosco and M. Huerta, “Entanglement and alpha entropies for a massive Dirac field in two dimensions,” J. Stat. Mech. 0507
2005
Cited alongside, same era.
T. Nishioka, S. Ryu and T. Takayanagi, “Holographic Entanglement Entropy: An Overview,” J. Phys. A 42
Original
2006
Cited alongside, same era.
See for example J. Eisert, M. Cramer, M.B. Plenio, “Area laws for the entanglement entropy - a review,” Rev. Mod. Phys. 82
Original
2008
Cited alongside, same era.
H. Casini and M. Huerta, “Remarks on the entanglement entropy for disconnected regions,” JHEP 0903
Original
2009
Cited alongside, same era.
N. D. Birrell and P. C. W. Davies, “Quantum Fields in Curved Space,” Cambridge Monogr. Math. Phys., Cambridge (1982); L. Parker and D. Toms, “Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity”, Cambridge University Press, Cambridge (2009)

Then

D. N. Kabat and M. J. Strassler, “A Comment on entropy and area,” Phys. Lett. B 329
Original
2013
Later among the works it cites.
A. Lewkowycz, R. C. Myers and M. Smolkin, “Observations on entanglement entropy in massive QFT’s,” JHEP 1304
Original
2013
Later among the works it cites.
D. D. Blanco, H. Casini, L. Y. Hung and R. C. Myers, “Relative Entropy and Holography,” JHEP 1308
Original
2013
Later among the works it cites.
H. Liu and M. Mezei, “Probing renormalization group flows using entanglement entropy,” JHEP 1401
Original
2014
Closest in time.
V. Rosenhaus and M. Smolkin, “Entanglement entropy, planar surfaces, and spectral functions,” JHEP 1409
Original

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2014

Area terms in entanglement entropy

Casini, Horacio, Mazzitelli, F. D., Testé, Eduardo

Understand

We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the term involving a correlator of traces of the stress tensor in Adler-Zee formula for the renormalization of the Newton constant.

We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions.
We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature.
We also discuss an application to the F-theorem.

Built on

K. Osterwalder and R. Schrader, “Axioms For Euclidean Green’s Functions,” Commun. Math. Phys. 31
1973
Earlier work this paper cites.
A. Zee, “Spontaneously Generated Gravity,” Phys. Rev. D 23
1981
Earlier work this paper cites.
S. L. Adler, “Einstein Gravity as a Symmetry Breaking Effect in Quantum Field Theory,” Rev. Mod. Phys. 54
1983
Earlier work this paper cites.
H. Muratani and S. Wada, “The Divergent Parts Of Quantum Fluctuation In The Curved Space From The Adler-zee Formulae,” Phys. Rev. D 29
1984
Earlier work this paper cites.
A. Cappelli, D. Friedan and J. I. Latorre, “C theorem and spectral representation,” Nucl. Phys. B 352
1991
Earlier work this paper cites.
R. Haag, “Local quantum physics: Fields, particles, algebras,” Berlin, Germany: Springer (1992). (Texts and monographs in physics)
1992
Earlier work this paper cites.
L. Bombelli, R. K. Koul, J. Lee and R. D. Sorkin, “A Quantum Source of Entropy for Black Holes,” Phys. Rev. D 34
1993
Earlier work this paper cites.
L. Susskind and J. Uglum, “Black hole entropy in canonical quantum gravity and superstring theory,” Phys. Rev. D 50
1994
Earlier work this paper cites.
D. V. Fursaev and S. N. Solodukhin, “On one loop renormalization of black hole entropy,” Phys. Lett. B 365
Original
1995
Earlier work this paper cites.
F. Larsen and F. Wilczek, “Renormalization of black hole entropy and of the gravitational coupling constant,” Nucl. Phys. B 458
1996
Earlier work this paper cites.
L. Susskind, “The World as a hologram,” J. Math. Phys. 36
1998
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech. 0406
2004
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement and alpha entropies for a massive scalar field in two dimensions,” J. Stat. Mech. 0512
2005
Earlier work this paper cites.

Similar

H. Casini, C. D. Fosco and M. Huerta, “Entanglement and alpha entropies for a massive Dirac field in two dimensions,” J. Stat. Mech. 0507
2005
Cited alongside, same era.
T. Nishioka, S. Ryu and T. Takayanagi, “Holographic Entanglement Entropy: An Overview,” J. Phys. A 42
Original
2006
Cited alongside, same era.
See for example J. Eisert, M. Cramer, M.B. Plenio, “Area laws for the entanglement entropy - a review,” Rev. Mod. Phys. 82
Original
2008
Cited alongside, same era.
H. Casini and M. Huerta, “Remarks on the entanglement entropy for disconnected regions,” JHEP 0903
Original
2009
Cited alongside, same era.
N. D. Birrell and P. C. W. Davies, “Quantum Fields in Curved Space,” Cambridge Monogr. Math. Phys., Cambridge (1982); L. Parker and D. Toms, “Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity”, Cambridge University Press, Cambridge (2009)