Bulk entanglement entropy in perturbative excited states

Belin, Alexandre; Iqbal, Nabil; Lokhande, Sagar F.

doi:10.21468/scipostphys.5.3.024

Cited by 42 publications

(123 citation statements)

References 64 publications

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“…(22) of [47]. 27 The result (6.20) reduces to similar trigonometric expressions for many values of ∆; they always diverge as a → π. λ (1) (x)O(x) and expand to second order, we get…”

Section: Explicit Calculationmentioning

confidence: 81%

“…Assuming this works, we would like to understand what constraints the bulk state must satisfy, i.e., whether it is possible to show that some quantum version of the gravitational constraints must be satisfied. This was done for general linear perturbations in [26], and very explicitly for a different class of (one-particle) states in [27]; but as we will see, there are qualitatively new features in the case of non-linear multi-trace perturbations. 6…”

Section: Reproducing Subleading Entanglement Entropies Via Gravitymentioning

confidence: 83%

“…We would like to check, with as few assumptions as possible, that the CFT entanglement entropy for a ball-shaped region can be reproduced by an auxiliary gravity calculation via the quantum RT formula (1.2). An interesting case where this has been accomplished at the quantum level is the paper [27], which demonstrates such a matching in the case of a single scalar particle in AdS 3 , where the CFT region is taken to be a small interval.…”

Section: Cft Entanglement Entropy and The Quantum Rt Formulamentioning

confidence: 99%

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Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories

Haehl

Mintun

Pollack

et al. 2019

J. High Energ. Phys.

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We consider CFT states defined by adding nonlocal multi-trace sources to the Euclidean path integral defining the vacuum state. For holographic theories, we argue that these states correspond to states in the gravitational theory with a good semiclassical description but with a more general structure of bulk entanglement than states defined from single-trace sources. We show that at leading order in large N , the entanglement entropies for any such state are precisely the same as those of another state defined by appropriate single-trace effective sources; thus, if the leading order entanglement entropies are geometrical for the single-trace states of a CFT, they are geometrical for all the multi-trace states as well. Next, we consider the perturbative calculation of 1/N corrections to the CFT entanglement entropies, demonstrating that these show qualitatively different features, including non-analyticity in the sources and/or divergences in the naive perturbative expansion. These features are consistent with the expectation that the 1/N corrections include contributions from bulk entanglement on the gravity side. Finally, we investigate the dynamical constraints on the bulk geometry and the quantum state of the bulk fields which must be satisfied so that the entropies can be reproduced via the quantum-corrected Ryu-Takayanagi formula. arXiv:1904.01584v2 [hep-th] 5 Jun 2019 7 CFT entanglement entropy and the quantum RT formula 42 7.1 Basic identities 42 7.2 Quantum-gravitational constraints 49 7.2.1 Direct argument for the equality of relative entropies 50 7.2.2 Quantum-corrected Einstein equation: first order in the graviton operator 53 7.2.3 Second order "quantum" Einstein equations 56 8 Summary and discussion 57 -i -A General correlation functions in the effective geometry 59 B Divergent relative entropy for perturbed CFT thermal states 62 B.1 Relative entropy in thermal states using replica trick 62 B.2 Relative entropy in thermal states with finite spatial separation 66 C Perturbative relative entropy at k-th order 67 1 Here, N is a parameter related to the number of degrees of freedom in the theory; for example, the rank of a gauge group, or some power of the central charge in a CFT. 2 In [13] this argument was generalized to linearized equations about more general background states. 3The second-order calculation is sensitive to two central charge parameters in the CFT, characterizing respectively the vacuum entanglement of balls and the stress tensor two-point function. If these a-and c-type central charges are equal, the gravitational equations are those of pure Einstein gravity, otherwise the auxiliary gravitational theory involves higher derivatives [15,16].5 Similar observations regarding the breakdown of naive perturbation theory have been made recently in [23,24]. 6 See also [28][29][30][31] for similar recent constructions. 10 We thank O. Parrikar for raising this point.

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“…(22) of [47]. 27 The result (6.20) reduces to similar trigonometric expressions for many values of ∆; they always diverge as a → π. λ (1) (x)O(x) and expand to second order, we get…”

Section: Explicit Calculationmentioning

confidence: 81%

Section: Reproducing Subleading Entanglement Entropies Via Gravitymentioning

confidence: 83%

Section: Cft Entanglement Entropy and The Quantum Rt Formulamentioning

confidence: 99%

See 1 more Smart Citation

Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories

Haehl

Mintun

Pollack

et al. 2019

J. High Energ. Phys.

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show abstract

“…In QFT, it is fundamental for the study of relative entropy [17,18] and its many applications to energy and information inequalities [19][20][21]. In the context of the AdS/CFT correspondence, it is instrumental in the program of reconstructing a gravitational bulk from the holographic data [22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Entanglement Spectrum of Chiral Fermions on the Torus

Fries

Reyes

2019

Phys. Rev. Lett.

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We determine the reduced density matrix of chiral fermions on the torus, for an arbitrary set of disjoint intervals and generic torus modulus. We find the resolvent, which yields the modular Hamiltonian in each spin sector. Together with a local term, it involves an infinite series of bi-local couplings, even for a single interval. These accumulate near the endpoints, where they become increasingly redshifted. Remarkably, in the presence of a zero mode, this set of points "condenses" within the interval at low temperatures, yielding continuous non-locality. * Electronic address: pascal.fries@physik.uni-wuerzburg.de † Electronic address: iareyes@uc.cl

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“…I thank the referee for mentioning this important point 17. this statement is of course no longer valid for the CFT in a generic state, as for example in an exited state, see[8], or a thermal state.…”

mentioning

confidence: 99%

A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections

Prudenziati

2019

J. High Energ. Phys.

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We use the formalism of geodesic Witten diagrams to study the holographic realization of the conformal block expansion for entanglement entropy of two disjoint intervals. The agreement between the Ryu-Takayanagi formula and the identity block contribution has a dual realization as the product of bulk to boundary propagators. Quantum bulk corrections instead arise from stripped higher order diagrams and back-reaction effects; these are also mapped to the structure for G 0 N terms found in [15], with the former identified as the bulk entanglement entropy across the Ryu-Takayanagi surfaces. An independent derivation of this last statement is provided by implementing a twist-line formalism in the bulk, and additional checks from the computation of mutual information and single interval entanglement entropy. Finally an interesting correspondence is found between the recently proposed holographic entanglement of purification, and an approximated form for certain 1/c Renyi entropies corrections.

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Bulk entanglement entropy in perturbative excited states

Cited by 42 publications

References 64 publications

Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories

Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories

Entanglement Spectrum of Chiral Fermions on the Torus

A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections

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