Universality in the Shape Dependence of Holographic Rényi Entropy for General Higher Derivative Gravity

Abstract

We consider higher derivative gravity and obtain universal relations for the shape coefficients $(f_a,f_b,f_c)$ of the shape dependent universal part of the Rényi entropy for four dimensional CFTs in terms of the parameters $(c,t_2,t_4)$ of two-point and three-point functions of stress tensors. As a consistency check, these shape coefficients $f_a$ and $f_c$ satisfy the differential relation as derived previously for the Rényi entropy. Interestingly, these holographic relations also apply to weakly coupled conformal field theories such as theories of free fermions and vectors but are violated by theories of free scalars. The mismatch of $f_a$ for scalars has been observed in the literature and is due to certain delicate boundary contributions to the modular Hamiltonian. Interestingly, we find a combination of our holographic relations which are satisfied by all free CFTs including scalars. We conjecture that this combined relation is universal for general CFTs in four dimensional spacetime. Finally, we find there are similar universal laws for holographic Rényi entropy in general dimensions.

arXiv comment32 pages,0 figures, references added, appendix added, accepted for publication in JHEP

References in corpus (33)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Stress Tensor for Anti-de Sitter Gravity
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Generalized gravitational entropy
• Building up spacetime with quantum entanglement
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Conformal collider physics: Energy and charge correlations
• Gravitation from Entanglement in Holographic CFTs
• Gravitational Dynamics From Entanglement "Thermodynamics"
• The Gravity Dual of Renyi Entropy
• Holographic GB gravity in arbitrary dimensions
• Entanglement entropy, conformal invariance and extrinsic geometry
• Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
• Holographic Calculations of Renyi Entropy
• Diffeomorphisms and Holographic Anomalies
• Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity
• Universality of corner entanglement in conformal field theories
• Entanglement Entropy, Trace Anomalies and Holography
• Hamiltonian formulation of f(Riemann) theories of gravity
• Renyi Entropies for Free Field Theories
• Rényi entropy and conformal defects
• Universality in the geometric dependence of Renyi entropy
• Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method
• Universal corner entanglement from twist operators
• Shape Dependence of Holographic Rényi Entropy in General Dimensions
• Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
• Entanglement Renyi Entropies in Conformal Field Theories and Holography
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities
• Higher Derivative Corrections to R-charged Black Holes: Boundary Counterterms and the Mass-Charge Relation
• Holographic stress tensor at finite coupling
• A Note on Holographic Weyl Anomaly and Entanglement Entropy
• Gravity duals of boundary cones

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• Effective Action, Spectrum and First Law of Wedge Holography
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• CFT correlators from shape deformations in Cubic Curvature Gravity
• Non-analyticity of holographic Rényi entropy in Lovelock gravity
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• Shape Deformations of Charged Rényi Entropies from Holography