Relative entropy in higher spin holography

Abstract

We examine relative entropy in the context of the higher-spin/CFT duality. We consider 3$d$ bulk configurations in higher spin gravity which are dual to the vacuum and a high temperature state of a CFT with $\mathcal{W}$-algebra symmetries in presence of a chemical potential for a higher spin current. The relative entropy between these states is then evaluated using the Wilson line functional for holographic entanglement entropy. In the limit of small entangling intervals, the relative entropy should vanish for a generic quantum system. We confirm this behaviour by showing that the difference in the expectation values of the modular Hamiltonian between the states matches with the difference in the entanglement entropy in the short-distance regime. Additionally, we compute the relative entropy of states corresponding to smooth solutions in the $SL(2,\mathbb{Z})$ family with respect to the vacuum.

arXiv comment29 pages. Published version. All relative entropies are calculated with respect to the vacuum

References in corpus (60)

• Large N Field Theories, String Theory and Gravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• A Stress Tensor for Anti-de Sitter Gravity
• Aspects of Holographic Entanglement Entropy
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Entanglement entropy and conformal field theory
• Towards a derivation of holographic entanglement entropy
• Evolution of Entanglement Entropy in One-Dimensional Systems
• The Role of Relative Entropy in Quantum Information Theory
• AdS Dual of the Critical O(N) Vector Model
• AdS3 Black Holes and a Stringy Exclusion Principle
• Holographic Entanglement Entropy: An Overview
• Holographic c-theorems in arbitrary dimensions
• Massless Higher Spins and Holography
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Gravitation from Entanglement in Holographic CFTs
• An AdS_3 Dual for Minimal Model CFTs
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Relative Entropy and Holography
• Minimal Model Holography
• Thermodynamical Property of Entanglement Entropy for Excited States
• Symmetries of Holographic Minimal Models
• Entanglement Temperature and Entanglement Entropy of Excited States
• Higher Spin Black Holes
• Black holes in three dimensional higher spin gravity: A review
• A Black Hole Farey Tail
• Spacetime Geometry in Higher Spin Gravity
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Higher Spin Black Holes from CFT
• Large N=4 Holography
• Partition Functions of Holographic Minimal Models
• Generalized Black Holes in Three-dimensional Spacetime
• Partition functions of higher spin black holes and their CFT duals
• Thermodynamics of Higher Spin Black Holes in AdS${}_3$
• Relative Entropies in Conformal Field Theory
• Entanglement Entropy and Higher Spin Holography in AdS${}_3$
• ABJ Triality: from Higher Spin Fields to Strings
• Higher spin gravity in 3D: black holes, global charges and thermodynamics
• Thermodynamics of higher spin black holes in 3D
• Entropic Counterpart of Perturbative Einstein Equation
• The semiclassical limit of W_N CFTs and Vasiliev theory
• Higher spin entanglement entropy from CFT
• W Symmetry and Integrability of Higher spin black holes
• Constraining gravity using entanglement in AdS/CFT
• Observables and Microscopic Entropy of Higher Spin Black Holes
• Matching four-point functions in higher spin AdS_3/CFT_2
• Probing higher spin black holes from CFT
• A universal correction to higher spin entanglement entropy
• A note on conical solutions in 3D Vasiliev theory
• Conical Defects in Higher Spin Theories
• Phase Structure of Higher Spin Black Hole
• Modular Properties of 3D Higher Spin Theory
• Brief review on higher spin black holes
• On the partition functions of higher spin black holes
• Phase Structure of Higher Spin Black Holes

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