Shape Dependence of Holographic Rényi Entropy in General Dimensions

Abstract

We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for $d=3,\dots ,6$ spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove a set of conjectures in the literature regarding the relations between the Rényi shape dependence and the conformal weight of the twist operator. We also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.

33 pages, 4 figures

References in corpus (18)

• Towards a derivation of holographic entanglement entropy
• Conformal collider physics: Energy and charge correlations
• Holographic c-theorems in arbitrary dimensions
• Viscosity Bound and Causality Violation
• Seeing a c-theorem with holography
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• Entanglement Entropy in the O(N) model
• Universality of corner entanglement in conformal field theories
• Entanglement entropy across a deformed sphere
• Universality in the geometric dependence of Renyi entropy
• On shape dependence of holographic mutual information in AdS4
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Renyi Entropy and Geometry
• Gravity duals of boundary cones
• Gravitational dual of the Rényi twist displacement operator

Cited by in corpus (40)

• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• A General Proof of the Quantum Null Energy Condition
• Universality at large transverse spin in defect CFT
• Aspects of capacity of entanglement
• All higher-curvature gravities as Generalized quasi-topological gravities
• Holographic studies of Einsteinian cubic gravity
• Line defects and radiation in $\mathcal{N}=2$ theories
• Superconformal surfaces in four dimensions
• An Exact Construction of Codimension two Holography
• Bootstrapping line defects with $O(2)$ global symmetry
• Monodromy Defects from Hyperbolic Space
• The Holographic Shape of Entanglement and Einstein's Equations
• Exact Bremsstrahlung functions in ABJM theory
• Monodromy Defects in Free Field Theories
• Comments on Squashed-sphere Partition Functions
• Universality for Shape Dependence of Casimir Effects from Weyl Anomaly
• Universality in the Shape Dependence of Holographic Rényi Entropy for General Higher Derivative Gravity
• Local measures of entanglement in black holes and CFTs
• Generalizing the entanglement entropy of singular regions in conformal field theories
• Partition functions on slightly squashed spheres and flux parameters
• Higher-derivative holography with a chemical potential
• Casimir Effect, Weyl Anomaly and Displacement Operator in Boundary Conformal Field Theory
• Marginal deformations and defect anomalies
• Conformal Bootstrap near the edge
• Defect multiplets of N=1 supersymmetry in 4d
• Holographic entanglement entropy for perturbative higher-curvature gravities
• Shape dependence of renormalized holographic entanglement entropy
• Holographic two-point functions for Janus interfaces in the $D1/D5$ CFT
• Duality transformations and the entanglement entropy of gauge theories
• Cubic trihedral corner entanglement for a free scalar
• The energy-momentum multiplet of supersymmetric defect field theories
• Emitted Radiation and Geometry
• CFT correlators from shape deformations in Cubic Curvature Gravity
• Casimir Effect and Holographic Dual of Wedges
• The entanglement properties of holographic QCD model with a critical end point
• Non-analyticity of holographic Rényi entropy in Lovelock gravity
• Proof of Renyi QNEC for free fermions
• Subsystem entropy in 2d CFT and KdV ETH
• Higher-Curvature Gravity, Black Holes and Holography
• Shape Deformations of Charged Rényi Entropies from Holography