Entanglement Rényi entropies in conformal field theories and holography

Fursaev, Dmitri V.

doi:10.1007/jhep05(2012)080

Cited by 58 publications

(83 citation statements)

References 51 publications

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“…This result can be independently confirmed using the vector heat kernel on manifolds with a conical singularity [22], [23]. However, to our knowledge, a field theory calculation via the approach developed in [13] reproducing this result is absent (besides directly adopting the anomaly coefficients).…”

Section: Introductionmentioning

confidence: 51%

“…The main reason we consider a different approach in this paper to study the entanglement entropy of gauge fields instead of adopting the traditional replica method is that one is already able to obtain the expected central charge-entropy relation (8) using the conical method [22]. On the other hand, it is well-known that the conical singularity causes subtle issues such as generating a contact term [32].…”

Section: Conical Contact Entropymentioning

confidence: 99%

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Central charge and entangled gauge fields

Huang

2015

Phys. Rev. D

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Entanglement entropy of gauge fields is calculated using the partition function in curved spacetime with boundary. Deriving a Gibbons-Hawking like term from a BRST action produces a Wald entropy like codimension-2 surface term. It is further suggested that boundary degrees of freedom localized on the entanglement surface generated from the gauge redundancy could be used to resolve a subtle mismatch in a universal conformal anomaly-entanglement entropy relation. Introduction:In spite of being perhaps the weirdest consequence from quantum mechanics [1], the concept of entanglement plays an important role in many areas of physics: A key ingredient in quantum information, an order parameter in the phase transition in many-body systems [2], a measure of renormalization group flow in quantum field theories [3]. The entanglement entropy is also suggested as the origin of the black hole entropy [4], [5]. Decomposing the full Hilbert space into pieces A and its complement B,

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Section: Introductionmentioning

confidence: 51%

Section: Conical Contact Entropymentioning

confidence: 99%

Central charge and entangled gauge fields

Huang

2015

Phys. Rev. D

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“…We have extracted the logarithimic term from the Wald entropy as it requires only information about the bulk space time around the boundary. Although we have demonstrated that the regularized squashed cones of [26] can be used to compute EE, a naive application of this procedure would not work for Renyi entropies [10,52,53] for general n although the starting metric is regular. Except near n = 1, where we saw that the universality in Renyi entropy [10,47,49,50] pertaining to ∂ n S n | n=1 bears out, the result for a general n would be regularization dependent -for instance we will need to know details about f (r, b) away from r = 0.…”

Section: Jhep01(2014)021mentioning

confidence: 99%

On generalized gravitational entropy, squashed cones and holography

Bhattacharyya

Sharma

Sinha

2014

J. High Energ. Phys.

107

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Abstract:We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.

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“…For the theory consisting of n s free real scalars, n f free Weyl fermions and n v free vectors, the functions f a (n) and f c (n) have been calculated explicitly in [8,15,[36][37][38][39]. We list the results as follows:…”

Section: The Story Of Free Cftsmentioning

confidence: 99%

Universality in the shape dependence of holographic Rényi entropy for general higher derivative gravity

Chu

Miao

2016

J. High Energ. Phys.

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We consider higher derivative gravity and obtain universal relations for the shape coefficients (f a , f b , f c ) of the shape dependent universal part of the Rényi entropy for four dimensional CFTs in terms of the parameters (c, t 2 , t 4 ) of two-point and three-point functions of stress tensors. As a consistency check, these shape coefficients f a and f c satisfy the differential relation as derived previously for the Rényi entropy. Interestingly, these holographic relations also apply to weakly coupled conformal field theories such as theories of free fermions and vectors but are violated by theories of free scalars. The mismatch of f a for scalars has been observed in the literature and is due to certain delicate boundary contributions to the modular Hamiltonian. Interestingly, we find a combination of our holographic relations which are satisfied by all free CFTs including scalars. We conjecture that this combined relation is universal for general CFTs in four dimensional spacetime. Finally, we find there are similar universal laws for holographic Rényi entropy in general dimensions.

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Entanglement Rényi entropies in conformal field theories and holography

Cited by 58 publications

References 51 publications

Central charge and entangled gauge fields

Central charge and entangled gauge fields

On generalized gravitational entropy, squashed cones and holography

Universality in the shape dependence of holographic Rényi entropy for general higher derivative gravity

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