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Renormalized holographic entanglement entropy in Lovelock gravity
High Energy Physics - Theory · Submitted 26 Mar 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our results illustrate the notable improvement that the Kounterterm method affords over other approaches, as it is non-perturbative and does not require that the Lovelock theory has limiting Einstein behavior.
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The abstract, sentence by sentence
We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity. It is known that the holographic EE in Lovelock gravity is given by the Jacobson-Myers (JM) functional. As usual, due to the divergent Weyl factor in the Fefferman-Graham expansion of the boundary metric for Asymptotically AdS spaces, this entropy functional is infinite. By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for AAdS spacetimes, we propose a new renormalization prescription for the Jacobson-Myers functional. We then explicitly show the cancellation of divergences in the EE up to next-to-leading order in the holographic radial coordinate, for the case of spherical entangling surfaces. Using this new renormalization prescription, we directly find the $C-$function candidates for odd and even dimensional CFTs dual to Lovelock gravity. Our results illustrate the notable improvement that the Kounterterm method affords over other approaches, as it is non-perturbative and does not require that the Lovelock theory has limiting Einstein behavior.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity. | contribution 0.95 | 0.90 | 0.06 | asserted 0.89 |
| s1 | It is known that the holographic EE in Lovelock gravity is given by the Jacobson-Myers (JM) functional. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s2 | As usual, due to the divergent Weyl factor in the Fefferman-Graham expansion of the boundary metric for Asymptotically AdS spaces, this entropy functional is infinite. | background 0.99 | 0.05 | 0.02 | asserted 1.00 |
| s3 | By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for AAdS spacetimes, we propose a new renormalization prescription for the Jacobson-Myers functional. | method 0.53 | 0.84 | 0.17 | asserted 0.84 |
| s4 | We then explicitly show the cancellation of divergences in the EE up to next-to-leading order in the holographic radial coordinate, for the case of spherical entangling surfaces. | result 0.98 | 0.95 | 0.17 | asserted 1.00 |
| s5 | Using this new renormalization prescription, we directly find the $C-$function candidates for odd and even dimensional CFTs dual to Lovelock gravity. | result 0.89 | 0.96 | 0.27 | asserted 1.00 |
| s6 | Our results illustrate the notable improvement that the Kounterterm method affords over other approaches, as it is non-perturbative and does not require that the Lovelock theory has limiting Einstein behavior. | interpretation 0.97 | 0.49 | 0.42 | asserted 0.98 |
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The paper
Original abstract
We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity. It is known that the holographic EE in Lovelock gravity is given by the Jacobson-Myers (JM) functional. As usual, due to the divergent Weyl factor in the Fefferman-Graham expansion of the boundary metric for Asymptotically AdS spaces, this entropy functional is infinite. By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for AAdS spacetimes, we propose a new renormalization prescription for the Jacobson-Myers functional. We then explicitly show the cancellation of divergences in the EE up to next-to-leading order in the holographic radial coordinate, for the case of spherical entangling surfaces. Using this new renormalization prescription, we directly find the $C-$function candidates for odd and even dimensional CFTs dual to Lovelock gravity. Our results illustrate the notable improvement that the Kounterterm method affords over other approaches, as it is non-perturbative and does not require that the Lovelock theory has limiting Einstein behavior.
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References
How the literature uses it
8 arXiv papers cite this in 8 sentences
Papers citing it · 7 sentences without a confident label
Cites it as background 1 paper
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Naturally, much work has been done on extending holographic $c$-theorems to include higher-derivative corrections [ref] .
Explorations in Precision Holography and Higher-derivative Supergravity · Discussion · 0.85
What it cites · 66 sentences without a confident label
Builds on 3 papers
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Especially in the case of even-dimensional bulks, a useful rewriting of the renormalized action in terms of a polynomial on the AdS curvature of the manifold is obtained, which is a generalization of the renormalized volume formula proposed for Einstein-AdS [ref] .
Einstein-AdS action, renormalized volume/area and holographic Renyi entropies · Preliminaries: Lovelock Gravity and factorized equations of motion · 0.98
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[ref] , to the entire Lovelock class.
Renormalization of Entanglement Entropy from topological terms · Topological reinterpretation of HEE in odd-dimensional CFTs · 0.99
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[ref] , to the entire Lovelock class.
Topological terms, AdS_2n gravity and renormalized Entanglement Entropy of holographic CFTs · Topological reinterpretation of HEE in odd-dimensional CFTs · 0.99
Uses the method or tool of 6 papers
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We obtain this by making use of the Kounterterm renormalization procedure [ref] .
Universal regularization prescription for Lovelock AdS gravity · Introduction · 1.00
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We obtain this by making use of the Kounterterm renormalization procedure [ref] .
Mass, Angular Momentum and Thermodynamics in Four-Dimensional Kerr-AdS Black Holes · Introduction · 1.00
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We obtain this by making use of the Kounterterm renormalization procedure [ref] .
Regularization of odd-dimensional AdS gravity: Kounterterms · Introduction · 1.00
Compares with 8 papers
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We note that sometimes it is more convenient to write [equation] in order to immediately identify the coefficient $c_j$ of the $ℱ ^j$ term as [equation] In the Einstein-AdS case, where $α_0$ and $α_1$ are given in [ref], with $α_p>1=0$, the expression [ref] matches that obtained previously for the definition of renormalized volume [ref] .
Einstein-AdS action, renormalized volume/area and holographic Renyi entropies · The $P(ℱ)$ formulation for even-dimensional AAdS manifolds · 0.83
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This is identically equal to one in the case of Einstein-AdS gravity, recovering previous results in the Einstein-AdS case [ref] .
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs · Renormalized HEE for ball-shaped regions and $C-$function candidates · 0.86
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[ref] and [ref], respectively, where we note that the C-function candidate is always proportional to the one for Einstein-AdS gravity, with a coupling-dependent factor, commensurate with the recent literature [ref] .
Holographic entanglement entropy for perturbative higher-curvature gravities · Conclusions · 0.84
Cites as background 19 papers
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The Ryu-Takayanagi (RT) prescription [ref] allows one to compute the entanglement entropy for a region $A$ in a conformal field theory (CFT) dual to Einstein gravity (and additional matter fields) in terms of the area $𝒜(Σ_A)$ of a surface $Σ_A$ of minimal area in the bulk that is homologous to $A$ [equation] known as the Holographic Entanglement Entropy (HEE) formula, where $G$ is the gravitational constant.
Holographic Derivation of Entanglement Entropy from AdS/CFT · Introduction · 0.81
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In the case of Einstein-AdS [ref] , $M_d+1^( α)$ is the backreacted manifold sourced by a codimension-2 cosmic brane with tension $T=( 1-α) /4G$, coupled to the ambient geometry through the Nambu-Goto (NG) action.
Holographic Entanglement Entropy for General Higher Derivative Gravity · Introduction · 0.80
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They have been used to investigate interesting CFT physics [ref] that in some cases is quite universal, applicable to very general CFTs [ref] .
Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity · Introduction · 0.84
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