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#### A holographic proof of the universality of corner entanglement for CFTs

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1507.06283.pdf

(Preprint), 314KB

JHEP10(2015)038.pdf

(Publisher version), 407KB

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##### Citation

Miao, R. X. (2015). A holographic proof of the universality of corner entanglement
for CFTs.* Journal of high energy physics: JHEP,* *2015*(10):
038. doi:10.1007/JHEP10(2015)038.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0028-9C90-1

##### Abstract

There appears a universal logarithmic term of entanglement entropy, i.e.,

$-a(\Omega) \log(H/\delta)$, for 3d CFTs when the entangling surface has a

sharp corner. $a(\Omega)$ is a function of the corner opening angle and behaves

as $a(\Omega\to \pi)\simeq \sigma (\pi-\Omega)^2$ and $a(\Omega\to 0)\simeq

\kappa/\Omega$, respectively. Recently, it is conjectured that

$\sigma/C_T=\pi^2/24 $, where $C_T$ is central charge in the stress tensor

correlator, is universal for general CFTs in three dimensions. In this paper,

by applying the general higher curvature gravity, we give a holographic proof

of this conjecture. We also clarify some interesting problems. Firstly, we find

that, in contrast to $\sigma/C_T$, $\kappa/C_T$ is not universal. Secondly, the

lower bound $a_E(\Omega)/C_T$ associated to Einstein gravity can be violated by

higher curvature gravity. Last but not least, we find that there are similar

universal laws for CFTs in higher dimensions. We give some holographic tests of

these new conjectures.

$-a(\Omega) \log(H/\delta)$, for 3d CFTs when the entangling surface has a

sharp corner. $a(\Omega)$ is a function of the corner opening angle and behaves

as $a(\Omega\to \pi)\simeq \sigma (\pi-\Omega)^2$ and $a(\Omega\to 0)\simeq

\kappa/\Omega$, respectively. Recently, it is conjectured that

$\sigma/C_T=\pi^2/24 $, where $C_T$ is central charge in the stress tensor

correlator, is universal for general CFTs in three dimensions. In this paper,

by applying the general higher curvature gravity, we give a holographic proof

of this conjecture. We also clarify some interesting problems. Firstly, we find

that, in contrast to $\sigma/C_T$, $\kappa/C_T$ is not universal. Secondly, the

lower bound $a_E(\Omega)/C_T$ associated to Einstein gravity can be violated by

higher curvature gravity. Last but not least, we find that there are similar

universal laws for CFTs in higher dimensions. We give some holographic tests of

these new conjectures.