Mutual information and the F-theorem

Casini, Horacio; Huerta, Marina; Myers, Robert C.; Yale, Alexandre

doi:10.1007/jhep10(2015)003

Cited by 145 publications

(198 citation statements)

References 109 publications

(305 reference statements)

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“…They also coincide with the constant (or logarithmic) term in the mutual information between two parallel planes, as was argued in [13] (see also [33]). Moreover, our holographic sum rule will provide a unified description of the d = 2 result, where the renormalization of the area term in EE is [34] …”

Section: Jhep03(2016)033supporting

confidence: 73%

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Holographic RG flows, entanglement entropy and the sum rule

Casini

Testé

Torroba

2016

J. High Energ. Phys.

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Abstract:We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d = 2 and in d > 2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.

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Section: Jhep03(2016)033supporting

confidence: 73%

“…However, our point is that no corrections to the constant term appear in the strip term for generic values of the powers, and our calculation will be enough to illustrate this. A similar calculation was carried out in [33].…”

Section: Jhep03(2016)033mentioning

confidence: 97%

Holographic RG flows, entanglement entropy and the sum rule

Casini

Testé

Torroba

2016

J. High Energ. Phys.

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“…It further coincides with the free energy of the same theory on S 3 [26]. As proven by Casini and Huerta [27] -see also [28] -a renormalized version of this quantity [29] is monotonously decreasing under the entire RG flow connecting two fixed points, and it coincides with F at fixed points. This "F-theorem" is one of the most celebrated applications of EE to QFT, and generalizes the earlier EE-based proof of the two-dimensional "ctheorem" [30,31].…”

supporting

confidence: 66%

“…Observe that the structure of (III.21) is very similar to the EE of a radius-R disk in a three-dimensional CFT in flat space, which reads S disk = BR/ − F , where F is independent of both the regulator and the disk's radius -when computed with sufficient care [28].…”

Section: Infinite Cylinder and Thin Torus Limitsmentioning

confidence: 77%

Holographic torus entanglement and its renormalization group flow

Bueno

Witczak-Krempa

2017

Phys. Rev. D

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We study the universal contributions to the entanglement entropy (EE) of 2+1d and 3+1d holographic conformal field theories (CFTs) on topologically non-trivial manifolds, focusing on tori. The holographic bulk corresponds to AdS-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2+1d, in the simple limit where the torus becomes a thin 1d ring, the EE reduces to a shape-independent constant 2γ. This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the RG flow of γ by defining a renormalized EE that 1) is applicable to general QFTs, 2) resolves the failure of the area law subtraction, and 3) is inspired by the F-theorem. We find that the renormalized γ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of non-uniqueness of such renormalized EEs both in 2+1d and 3+1d.

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“…This is done for square and v-shape which have the same volume. One can find that for small regions where the entropy scales with the volume the 13 See also [52] where a F -theorem is introduced in (2 + 1)-dimensions using mutual information for co-centric disks. Figure 12.…”

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confidence: 99%

Entanglement in Lifshitz-type quantum field theories

Mozaffar

Mollabashi

2017

J. High Energ. Phys.

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Abstract:We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz free scalar theory. We present simple intuitive arguments based on "non-local" effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the z → ∞ limit. We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior. In (2 + 1)-dimensions we also study some shape dependent aspects of entanglement. We argue that in the massless limit corner contributions are no more additive for large enough dynamical exponent due to non-local effects of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.

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Mutual information and the F-theorem

Cited by 145 publications

References 109 publications

Holographic RG flows, entanglement entropy and the sum rule

Holographic RG flows, entanglement entropy and the sum rule

Holographic torus entanglement and its renormalization group flow

Entanglement in Lifshitz-type quantum field theories

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