Higher Spin Entanglement and W_N Conformal Blocks

Abstract

Two-dimensional conformal field theories with extended $\mathcal{W}$-symmetry algebras have dual descriptions in terms of weakly coupled higher spin gravity in AdS${}_3$ at large central charge. Observables that can be computed and compared in the two descriptions include Rényi and entanglement entropies, and correlation functions of local operators. We develop techniques for computing these, in a manner that sheds light on when and why one can expect agreement between such quantities on each side of the duality. We set up the computation of excited state Rényi entropies in the bulk in terms of Chern-Simons connections, and show how this directly parallels the CFT computation of correlation functions. More generally, we consider the vacuum conformal block for general operators with $\Delta \sim c$. When two of the operators obey $\frac{\Delta }{c}\ll 1$, we show by explicit computation that the vacuum conformal block is computed by a bulk Wilson line probing an asymptotically AdS${}_3$ background with higher spin fields excited, the latter emerging as the effective bulk description of the excited state produced by the heavy operators. Among other things, this puts a previous proposal for computing higher spin entanglement entropy via Wilson lines on firmer footing, and clarifies its relation to CFT. We also study the corresponding computation in Toda theory and find that this provides yet another independent way to arrive at the same result.

56 pages

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• Bounding the Space of Holographic CFTs with Chaos
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• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• Virasoro conformal blocks in closed form
• Spinning Witten Diagrams
• Hawking from Catalan
• Higher-point conformal blocks and entanglement entropy in heavy states
• Holographic Quantum Circuits from Splitting/Joining Local Quenches
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Higher Spin Black Holes with Soft Hair
• Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators
• On the Chaos Bound in Rotating Black Holes
• On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles
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• Holographic conformal blocks from interacting Wilson lines
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• Holographic Conformal Partial Waves as Gravitational Open Wilson Networks
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Double Local Quenches in 2D CFTs and Gravitational Force
• Renyi Entropy for Local Quenches in 2D CFTs from Numerical Conformal Blocks
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Conformal blocks from Wilson lines with loop corrections
• Entanglement entropy at holographic interfaces
• Semi-classical BMS${}_3$ blocks and flat holography
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Holographic duals of large-c torus conformal blocks
• Holographic Calculation for Large Interval Rényi Entropy at High Temperature
• General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Wilson Lines and Ishibashi States in AdS${}_3$/CFT${}_2$
• Holographic Entanglement Entropy For a Large Class of States in 2D CFT
• Holographic Rényi Entropy of Single Interval on Torus: with W symmetry
• Anomalous dimensions from quantum Wilson lines
• Gravitational Wilson Lines in 3D de Sitter
• Subsystem distance after a local operator quench
• Eternal Higher Spin Black Holes: a Thermofield Interpretation
• Local quenches and quantum chaos from higher spin perturbations
• Multi-centered higher spin solutions from $W_N$ conformal blocks
• More on Wilson toroidal networks and torus blocks
• Higher spin entanglement entropy at finite temperature with chemical potential
• Late time Wilson lines
• Holographic Entanglement Entropy of Local Quenches in AdS${}_4$/CFT${}_3$: A Finite-Element Approach
• Chaos in Three-dimensional Higher Spin Gravity
• Extremal Higher Spin Black Holes
• CFT correlators, $\mathcal{W}$-algebras and Generalized Catalan Numbers
• Conical spaces, modular invariance and $c_{p,1}$ holography
• Higher-spin gauge theories in three spacetime dimensions
• What's the Point? Hole-ography in Poincare AdS
• Universal Local Operator Quenches and Entanglement Entropy
• On the universality of late-time correlators in semi-classical 2d CFTs
• Four-point conformal blocks with three heavy background operators
• Chern-Simons Gravity Dual of BCFT
• Worldline approach to semi-classical conformal blocks
• On skew tau-functions in higher spin theory
• Chaos bound in Bershadsky-Polyakov theory
• A note on the $\mathcal{N}=2$ super-${\mathcal{W}}_3$ holographic dictionary
• Generalized monodromy method in gauge/gravity duality
• Differential equations for classical Virasoro blocks with heavy and light operators
• Towards $W_3$ classical blocks with semi-degenerate operators