Renormalization of entanglement entropy from topological terms

Anastasiou, Giorgos; Araya, Ignacio J.; Olea, Rodrigo

doi:10.1103/physrevd.97.106011

Cited by 14 publications

(43 citation statements)

References 49 publications

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“…We note that in the tensionless limit, we recover our result for S ren EE given in Ref. [39]. Also, the resulting expression for S ren m , when multiplied by 4G, matches the formula given by Alexakis and Mazzeo for the renormalized area of a codimension-2 minimal surface embedded in a fourdimensional AAdS Einstein manifold, given in Ref.…”

Section: Action On Conical Orbifold As Deformed Volumesupporting

confidence: 86%

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Einstein-AdS action, renormalized volume/area and holographic Rényi entropies

Anastasiou

Araya

Arias

et al. 2018

J. High Energ. Phys.

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We exhibit the equivalence between the renormalized volume of asymptotically anti-de Sitter (AAdS) Einstein manifolds in four and six dimensions, and their renormalized Euclidean bulk gravity actions. The action is that of Einstein gravity, where the renormalization is achieved through the addition of a single topological term. We generalize this equivalence, proposing an explicit form for the renormalized volume of higher even-dimensional AAdS Einstein manifolds. We also show that evaluating the renormalized bulk gravity action on the conically singular manifold of the replica trick results in an action principle that corresponds to the renormalized volume of the regular part of the bulk, plus the renormalized area of a codimension-2 cosmic brane whose tension is related to the replica index. Renormalized Rényi entropy of odd-dimensional holographic CFTs can thus be obtained from the renormalized area of the brane with finite tension, including the effects of its backreaction on the bulk geometry. The area computation corresponds to an extremization problem for an enclosing surface that extends to the AdS boundary, where the newly defined renormalized volume is considered.

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Section: Action On Conical Orbifold As Deformed Volumesupporting

confidence: 86%

“…Considering the radial foliation along the holographic coordinate ρ with the corresponding FG asymptotic expansions as given in Refs. [39,40], and considering that the boundary of the manifold is the AdS boundary located at ρ = 0, we have that…”

Section: A Six-dimensional Conformal Invariantsmentioning

confidence: 99%

Einstein-AdS action, renormalized volume/area and holographic Rényi entropies

Anastasiou

Araya

Arias

et al. 2018

J. High Energ. Phys.

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“…In Ref. [1], we presented an alternative renormalization scheme for the entanglement entropy (EE) of 3D conformal field theories (CFTs) with 4D asymptotically anti-de Sitter (AAdS) gravity duals, in the context of the gauge/gravity duality [2][3][4]. The scheme considers the renormalized Einstein-AdS action obtained through the Kounterterms procedure [27][28][29][30][31], evaluated on a conically-singular manifold [33][34][35][36][37] defined via the Replica Trick [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Topological terms, AdS2n gravity, and renormalized entanglement entropy of holographic CFTs

2018

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We extend our topological renormalization scheme for entanglement entropy to holographic CFTs of arbitrary odd dimensions in the context of the AdS=CFT correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. The renormalized entanglement entropy thus obtained can be rewritten in terms of the Euler characteristic and the AdS curvature of the minimal surface. This prescription considers the use of the replica trick to express the renormalized entanglement entropy in terms of the renormalized gravitational action evaluated on the conically singular replica manifold extended to the bulk. This renormalized action is obtained in turn by adding the Chern form as the counterterm at the boundary of the 2n-dimensional asymptotically AdS bulk manifold. We explicitly show that, up to next-to-leading order in the holographic radial coordinate, the addition of this boundary term cancels the divergent part of the entanglement entropy. We discuss possible applications of the method for studying CFT parameters like central charges.

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“…In particular, in [57] the authors obtained the minimal D = 4 supergravity action plus boundary terms from the minimal Maxwell superalgebra sM 4 applying the Sexpansion procedure to osp(4|1). Let us observe, as a first hint towards this possible future study, that the action they ended up with can be also viewed as an Inönü-Wigner contraction of (59), and, on the other hand, it cannot be written as a sum of quadratic terms in the super field-strengths considered in [57].…”

Section: Supersymmetry Invariance Of the Theory In The Presence Of A mentioning

confidence: 96%

“…Then, we conjecture that the presence ofk ab , k ab , and ξ in the boundary of our theory, allowing to recover the supersymmetry invariance in the geometric approach, could also allow to regularize the (deformed) supergravity action in the holographic renormalization context. Furthermore, it would also be interesting to discuss our construction in the context of the recent works [59,60].…”

Section: Comments and Possible Developmentsmentioning

confidence: 99%

Generalized AdS-Lorentz deformed supergravity on a manifold with boundary

Banaudi

Ravera

2018

Eur. Phys. J. Plus

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The purpose of this paper is to explore the supersymmetry invariance of a particular supergravity theory, which we refer to as D = 4 generalized AdS-Lorentz deformed supergravity, in the presence of a non-trivial boundary. In particular, we show that the so-called generalized minimal AdS-Lorentz superalgebra can be interpreted as a peculiar torsion deformation of osp(4|1), and we present the construction of a bulk Lagrangian based on the aforementioned generalized AdS-Lorentz superalgebra. In the presence of a non-trivial boundary of space-time, that is when the boundary is not thought of as set at infinity, the fields do not asymptotically vanish, and this has some consequences on the invariances of the theory, in particular on supersymmetry invariance. In this work, we adopt the so-called rheonomic (geometric) approach in superspace and show that a supersymmetric extension of a Gauss-Bonnet like term is required in order to restore the supersymmetry invariance of the theory. The action we end up with can be recast as a MacDowell-Mansouri type action, namely as a sum of quadratic terms in the generalized AdS-Lorentz covariant super field-strengths. * alessandro.banaudi@mi.infn.it † lucrezia.ravera@mi.infn.it 1 The S-expansion method [31] is based on combining the multiplication law of a semigroup S with the structure constants of a Lie (super)algebra g, in such a way to end up with a new, larger, Lie (super)algebra g S = S × g, that is called the S-expanded (super)algebra (see also [32] for an analytic method for performing S-expansion).

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Renormalization of entanglement entropy from topological terms

Cited by 14 publications

References 49 publications

Einstein-AdS action, renormalized volume/area and holographic Rényi entropies

Einstein-AdS action, renormalized volume/area and holographic Rényi entropies

Topological terms, AdS2n gravity, and renormalized entanglement entropy of holographic CFTs

Generalized AdS-Lorentz deformed supergravity on a manifold with boundary

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