Renormalized entanglement entropy and curvature invariants

Taylor, Marika; Too, Linus

doi:10.1007/jhep12(2020)050

Cited by 11 publications

(8 citation statements)

References 35 publications

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“…where L is the AdS radius and G is the Newton constant -see also [40][41][42][43]. In this expression, 2Σ RT(A) ≡ Σ RT(A) ∪ Σ RT(A) is a closed surface embedded in R 3 which consists of a duplicated Ryu-Takayanagi surface [44]: the surface Σ RT(A) is just Σ RT(A) reflected with respect to the AdS boundary and joined along the entangling surface ∂A.…”

Section: Jhep10(2021)179mentioning

confidence: 99%

Disks globally maximize the entanglement entropy in 2 + 1 dimensions

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Casini

Andino

et al. 2021

J. High Energ. Phys.

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The entanglement entropy corresponding to a smooth region in general three-dimensional CFTs contains a constant universal term, −F ⊂ SEE. For a disk region, F|disk ≡ F0 coincides with the free energy on 𝕊3 and provides an RG-monotone for general theories. As opposed to the analogous quantity in four dimensions, the value of F generally depends in a complicated (and non-local) way on the geometry of the region and the theory under consideration. For small geometric deformations of the disk in general CFTs as well as for arbitrary regions in holographic theories, it has been argued that F is precisely minimized by disks. Here, we argue that F is globally minimized by disks with respect to arbitrary regions and for general theories. The proof makes use of the strong subadditivity of entanglement entropy and the geometric fact that one can always place an osculating circle within a given smooth entangling region. For topologically non-trivial entangling regions with nB boundaries, the general bound can be improved to F ≥ nBF0. In addition, we provide accurate approximations to F valid for general CFTs in the case of elliptic regions for arbitrary values of the eccentricity which we check against lattice calculations for free fields. We also evaluate F numerically for more general shapes in the so-called “Extensive Mutual Information model”, verifying the general bound.

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Section: Jhep10(2021)179mentioning

confidence: 99%

Disks globally maximize the entanglement entropy in 2 + 1 dimensions

Bueno

Casini

Andino

et al. 2021

J. High Energ. Phys.

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“…This relation holds in all even bulk spacetime dimensions, even though the expressions for the renormalized entanglement entropy become increasingly complex expressions of the Euler characteristic and curvature invariants of the entangling surface in higher dimensions [15]. The variation manifestly simplifies to just this one term for linear variations of a spherical surface around a background with zero Weyl curvature.…”

Section: Discussionmentioning

confidence: 99%

“…The variation manifestly simplifies to just this one term for linear variations of a spherical surface around a background with zero Weyl curvature. Working to higher order in the variations, and in more general setups, one should make use of the full form of the renormalized area in terms of Euler characteristic and curvature invariants in [15] to understand the underlying geometric structure.…”

Section: Discussionmentioning

confidence: 99%

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Generalised proofs of the first law of entanglement entropy

Taylor¹,

Too²

2021

Preprint

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In this paper we develop generalised proofs of the holographic first law of entanglement entropy using holographic renormalisation. These proofs establish the holographic first law for non-normalizable variations of the bulk metric, hence relaxing the boundary conditions imposed on variations in earlier works. Boundary and counterterm contributions to conserved charges computed via covariant phase space analysis have been explored previously. Here we discuss in detail how counterterm contributions are treated in the covariant phase approach to proving the first law. Our methodology would be applicable to generalizing other holographic information analyses to wider classes of gravitational backgrounds.

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“…It is simply because there are infinitely many microscopic degrees of freedom that contribute to EE. This type of UV divergences should be regularized by suitably renormalizing parameters in the background gravity [53][54][55][56][57][58]. In addition, further renormalizations are necessary for interacting theories.…”

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confidence: 99%

Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators

Iso,

Mori,

Sakai

2021

Preprint

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This is an extended version of the previous paper [1] to study entanglement entropy (EE) of a half space in interacting field theories. In the previous paper, we have proposed a novel method to calculate EE based on the notion of Z M gauge theory on Feynman diagrams, and shown that EE consists of two particular contributions, one from a renormalized two-point correlation function in the two-particle irreducible (2PI) formalism and another from interaction vertices. In this paper, we further investigate them in more general field theories and show that the non-Gaussian contributions from vertices can be interpreted as renormalized correlation functions of composite operators.

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Renormalized entanglement entropy and curvature invariants

Cited by 11 publications

References 35 publications

Disks globally maximize the entanglement entropy in 2 + 1 dimensions

Disks globally maximize the entanglement entropy in 2 + 1 dimensions

Generalised proofs of the first law of entanglement entropy

Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators

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