Charged Moments in $W_3$ Higher Spin Holography

Abstract

We consider the charged moments in $SL(3,\mathbb{R})$ higher spin holography, as well as in the dual two-dimensional conformal field theory with $W_3$ symmetry. For the vacuum state and a single entangling interval, we show that the $W_3$ algebra of the conformal field theory induces an entanglement $W_3$ algebra acting on the quantum state in the entangling interval. The algebra contains a spin 3 modular charge which commutes with the modular Hamiltonian. The reduced density matrix is characterized by the modular energy and modular charge, hence our definition of the charged moments is also with respect to these conserved quantities. We evaluate the logarithm of the charged moments perturbatively in the spin 3 modular chemical potential, by computing the corresponding connected correlation functions of the modular charge operator up to quartic order in the chemical potential. This method provides access to the charged moments without using charged twist fields. Our result matches known results for the charged moment obtained from the charged topological black hole picture in $SL(3,\mathbb{R})$ higher spin gravity. Since our charged moments are not Gaussian in the chemical potential any longer, we conclude that the dual $W_3$ conformal field theories must feature breakdown of equipartition of entanglement to leading order in the large $c$ expansion.

arXiv comment28 pages, no figures, v2: accepted for publication in JHEP

References in corpus (66)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Generalized gravitational entropy
• Building up spacetime with quantum entanglement
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• W-symmetry in Conformal Field Theory
• 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
• An AdS_3 Dual for Minimal Model CFTs
• Three-Dimensional Gravity Revisited
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Relative Entropy and Holography
• Holographic Entanglement Entropy
• Local bulk operators in AdS/CFT: a boundary view of horizons and locality
• Minimal Model Holography
• Symmetry-resolved entanglement in many-body systems
• Three-dimensional quantum geometry and black holes
• Entanglement hamiltonians in two-dimensional conformal field theory
• Holographic Calculations of Renyi Entropy
• Higher Spin Black Holes
• Constraints on symmetry from holography
• Triality in Minimal Model Holography
• Higher Spins & Strings
• Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
• Entwinement and the emergence of spacetime
• Holographic Charged Renyi Entropies
• Bounding the Space of Holographic CFTs with Chaos
• Higher Spin Black Holes from CFT
• Generalized Black Holes in Three-dimensional Spacetime
• Most general AdS_3 boundary conditions
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Partition functions of higher spin black holes and their CFT duals
• Physics at the entangling surface
• Thermodynamics of Higher Spin Black Holes in AdS${}_3$
• Towards metric-like higher-spin gauge theories in three dimensions
• Particle Number Fluctuations, Rényi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization
• Topological Complexity in AdS3/CFT2
• Symmetry resolved entanglement entropy of excited states in a CFT
• Holographic Subregion Complexity from Kinematic Space
• Higher spin gravity in 3D: black holes, global charges and thermodynamics
• ABJ Triality: from Higher Spin Fields to Strings
• Higher Spin Entanglement and W_N Conformal Blocks
• String Theory as a Higher Spin Theory
• Thermodynamics of higher spin black holes in 3D
• Symmetry resolved entanglement in integrable field theories via form factor bootstrap
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Finite-size corrections in critical symmetry-resolved entanglement
• Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$
• Classification of Quantum Hall Universality Classes by $W_{1+\infty }$ symmetry
• Boundary effects on symmetry resolved entanglement
• The action for higher spin black holes in three dimensions
• Towards a bulk description of higher spin SYK
• Higher spin entanglement entropy from CFT
• Entanglement of the $3$-State Potts Model via Form Factor Bootstrap: Total and Symmetry Resolved Entropies
• Equipartition of Entanglement in Quantum Hall States
• A universal correction to higher spin entanglement entropy
• Conformal perturbation theory and higher spin entanglement entropy on the torus
• Phase Structure of Higher Spin Black Hole
• Classical and Quantum W-Gravity
• Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy
• A new spin on entanglement entropy
• Monodromy methods for torus conformal blocks and entanglement entropy at large central charge
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
• Emergent universality in critical quantum spin chains: entanglement Virasoro algebra

Cited by in corpus (30)

• Symmetry-resolved Page curves
• Symmetry-resolved entanglement in a long-range free-fermion chain
• Symmetry-resolved entanglement in critical non-Hermitian systems
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits
• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
• Entanglement resolution of free Dirac fermions on a torus
• Multi-charged moments of two intervals in conformal field theory
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions
• Universal Thermal Corrections to Symmetry-Resolved Entanglement Entropy and Full Counting Statistics
• Two-Point Functions of Composite Twist Fields in the Ising Field Theory
• Symmetry-resolved modular correlation functions in free fermionic theories
• Page curve and symmetries
• A universal feature of charged entanglement entropy
• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Charge imbalance resolved Rényi negativity for free compact boson: Two disjoint interval case
• Dynamics of charge imbalance resolved negativity after a global quench in free scalar field theory
• Symmetry-resolved entanglement in fermionic systems with dissipation
• Symmetry Resolution in non-Lorentzian Field Theories
• Higher-spin gauge theories in three spacetime dimensions
• Multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals
• A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
• Symmetry Resolved Entanglement Entropy in Hyperbolic de Sitter Space
• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Symmetry-Resolved Entanglement Entropy in Higher Dimensions
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach
• Shape Deformations of Charged Rényi Entropies from Holography
• $2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals