Built on

J. L. Cardy, “Is There a c Theorem in Four-Dimensions?,” Phys. Lett. B 215
1988
Earlier work this paper cites.
H. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys. 231
1994
Earlier work this paper cites.
D. V. Fursaev and G. Miele, “Finite temperature scalar field theory in static de Sitter space,” Phys. Rev. D 49
1994
Earlier work this paper cites.
L. De Nardo, D. V. Fursaev and G. Miele, “Heat kernel coefficients and spectra of the vector Laplacians on spherical domains with conical singularities,” Class. Quant. Grav. 14
1997
Earlier work this paper cites.
M. Henningson and K. Skenderis, “The Holographic Weyl anomaly,” JHEP 9807
2000
Earlier work this paper cites.
F. Bastianelli, S. Frolov and A. A. Tseytlin, “Conformal anomaly of (2,0) tensor multiplet in six-dimensions and AdS / CFT correspondence,” JHEP 0002
2000
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech. 0406
2006
Earlier work this paper cites.
E. Fradkin and J. E. Moore, “Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement entropy in free quantum field theory,” J. Phys. A 42
Original
2007
Earlier work this paper cites.
T. Hirata and T. Takayanagi, “AdS/CFT and strong subadditivity of entanglement entropy,” JHEP 0702
2007
Earlier work this paper cites.
S. N. Solodukhin, “Entanglement entropy, conformal invariance and extrinsic geometry,” Phys. Lett. B 665
Original
2008
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
Original
2009
Earlier work this paper cites.

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2015

Universal entanglement for higher dimensional cones

Bueno, Pablo, Myers, Robert C.

Understand

The entanglement entropy of a generic $d$-dimensional conformal field theory receives a regulator independent contribution when the entangling region contains a (hyper)conical singularity of opening angle $\Omega$, codified in a function $a^{(d)}(\Omega)$.

In arXiv:1505.04804, we proposed that for three-dimensional conformal field theories, the coefficient $\sigma$ characterizing the smooth surface limit of such contribution ($\Omega\rightarrow \pi$) equals the stress tensor two-point function charge $C_{ T}$, up to a universal constant.
In this paper, we prove this relation for general three-dimensional holographic theories, and extend the result to general dimensions.
In particular, we show that a generalized coefficient $\sigma^{ (d)}$ can be defined for (hyper)conical entangling regions in the almost smooth surface limit, and that this coefficient is universally related to $C_{ T}$ for general holographic theories, providing a general formula for the ratio $\sigma^{ (d)}/C_{ T}$ in arbitrary dimensions.

Built on

J. L. Cardy, “Is There a c Theorem in Four-Dimensions?,” Phys. Lett. B 215
1988
Earlier work this paper cites.
H. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys. 231
1994
Earlier work this paper cites.
D. V. Fursaev and G. Miele, “Finite temperature scalar field theory in static de Sitter space,” Phys. Rev. D 49
1994
Earlier work this paper cites.
L. De Nardo, D. V. Fursaev and G. Miele, “Heat kernel coefficients and spectra of the vector Laplacians on spherical domains with conical singularities,” Class. Quant. Grav. 14
1997
Earlier work this paper cites.
M. Henningson and K. Skenderis, “The Holographic Weyl anomaly,” JHEP 9807
2000
Earlier work this paper cites.
F. Bastianelli, S. Frolov and A. A. Tseytlin, “Conformal anomaly of (2,0) tensor multiplet in six-dimensions and AdS / CFT correspondence,” JHEP 0002
2000
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Entanglement entropy and quantum field theory,” J. Stat. Mech. 0406
2006
Earlier work this paper cites.
E. Fradkin and J. E. Moore, “Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum,” Phys. Rev. Lett. 97
2006
Earlier work this paper cites.
H. Casini and M. Huerta, “Entanglement entropy in free quantum field theory,” J. Phys. A 42
Original
2007
Earlier work this paper cites.
T. Hirata and T. Takayanagi, “AdS/CFT and strong subadditivity of entanglement entropy,” JHEP 0702
2007
Earlier work this paper cites.
S. N. Solodukhin, “Entanglement entropy, conformal invariance and extrinsic geometry,” Phys. Lett. B 665
Original
2008
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
Original
2009
Earlier work this paper cites.