Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block

Abstract

We explore the structures of light cone and Regge limit singularities of $n$-point Virasoro conformal blocks in $c>1$ two-dimensional conformal field theories with no chiral primaries, using fusion matrix approach. These CFTs include not only holographic CFTs dual to classical gravity, but also their full quantum corrections, since this approach allows us to explore full $1/c$ corrections. As the important applications, we study time dependence of Renyi entropy after a local quench and out-of-time ordered correlator (OTOC) at late time. We first show that, the $n$-th ($n>2$) Renyi entropy after a local quench in our CFT grows logarithmically at late time, for any $c$ and any conformal dimensions of excited primary. In particular, we find that this behavior is independent of $c$, contrary to the expectation that the finite $c$ correction fixes the late time Renyi entropy to be constant. We also show that the constant part of the late time Renyi entropy is given by a monodromy matrix. We also investigate OTOCs by using the monodromy matrix. We first rewrite the monodromy matrix in terms of fusion matrix explicitly. By this expression, we find that the OTOC decays exponentially in time, and the decay rates are divided into three patterns, depending on the dimensions of external operators. We note that our result is valid for any $c>1$ and any external operator dimensions. Our monodromy matrix approach can be generalized to the Liouville theory and we show that the Liouville OTOC approaches constant in the late time regime. We emphasize that, there is a number of other applications of the fusion and the monodromy matrix approaches, such as solving the conformal bootstrap equation. Therefore, it is tempting to believe that the fusion and monodromy matrix approaches provide a key to understanding the AdS/CFT correspondence.

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References in corpus (106)

• A bound on chaos
• Generalized gravitational entropy
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Bounding scalar operator dimensions in 4D CFT
• The Analytic Bootstrap and AdS Superhorizon Locality
• Two-dimensional conformal field theory and the butterfly effect
• Two and three-point functions in Liouville theory
• Convexity and Liberation at Large Spin
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Liouville theory revisited
• Conformal Regge theory
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Solving the Schwarzian via the Conformal Bootstrap
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Large Spin Perturbation Theory
• Holographic Local Quenches and Entanglement Density
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Power-law out of time order correlation functions in the SYK model
• Universal Constraints on Conformal Operator Dimensions
• Quantum Entanglement of Local Operators in Conformal Field Theories
• A Universal Inequality for CFT and Quantum Gravity
• Entanglement Entropy in the O(N) model
• Entanglement Scrambling in 2d Conformal Field Theory
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• Bounding the Space of Holographic CFTs with Chaos
• Quantum Dimension as Entanglement Entropy in 2D CFTs
• Constraints on 2d CFT partition functions
• Characters and modular properties of permutation orbifolds
• Universal anomalous dimensions at large spin and large twist
• Conformal Bootstrap, Universality and Gravitational Scattering
• A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Analytic bootstrap at large spin
• Shockwave S-matrix from Schwarzian Quantum Mechanics
• Liouville theory with a central charge less than one
• Multipoint Conformal Blocks in the Comb Channel
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Entanglement of Local Operators in large N CFTs
• Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange
• Notes on Quantum Entanglement of Local Operators
• A Numerical Approach to Virasoro Blocks and the Information Paradox
• Bekenstein-Hawking Entropy as Topological Entanglement Entropy
• Probing thermality beyond the diagonal
• Holographic Phases of Renyi Entropies
• Holographic Quantum Circuits from Splitting/Joining Local Quenches
• Higher-point conformal blocks and entanglement entropy in heavy states
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
• ETH and Modular Invariance of 2D CFTs
• Classical conformal blocks via AdS/CFT correspondence
• Scrambling without chaos in RCFT
• A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
• A Semidefinite Program Solver for the Conformal Bootstrap
• Large spin systematics in CFT
• On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Anomalous Dimensions from Crossing Kernels
• Modular crossings, OPE coefficients and black holes
• Fractional Statistics and the Butterfly Effect
• Charged Renyi entropies and holographic superconductors
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Renyi Entropy for Local Quenches in 2D CFTs from Numerical Conformal Blocks
• Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ
• Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Universal corrections to entanglement entropy of local quantum quenches
• Conformal blocks from Wilson lines with loop corrections
• Genus Two Partition Functions and Renyi Entropies of Large c CFTs
• Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
• Thermalization after holographic bilocal quench
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Entanglement and chaos in warped conformal field theories
• Holographic duals of large-c torus conformal blocks
• Scattering effect on entanglement propagation in RCFTs
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Entanglement entropy in (1+1)D CFTs with multiple local excitations
• Permutation Orbifolds and Chaos
• Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits
• New Properties of Large-$c$ Conformal Blocks from Recursion Relation
• Evolution of Entanglement Entropy in Orbifold CFTs
• Out-of-Time-Ordered Correlators in $(T^2{)}^n/{\mathbb{Z}}_n$
• Superconformal blocks from Wilson lines with loop corrections
• Holographic Entanglement Entropy on Generic Time Slices
• Holographic Dual to Conical Defects: II. Colliding Ultrarelativistic Particles
• Phase transitions in 3D gravity and fractal dimension
• Large-c superconformal torus blocks
• The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
• Multi-centered higher spin solutions from $W_N$ conformal blocks
• Liouville field theory and log-correlated Random Energy Models
• Analytic continuation formulae for the BPZ conformal block
• Notes on Scrambling in Conformal Field Theory
• An Inelastic Bound on Chaos
• Recursive Representations of Arbitrary Virasoro Conformal Blocks
• Scrambling in Two-Dimensional Conformal Field Theories with Light and Smeared Operators
• Bootstrapping Pure Quantum Gravity in AdS3
• A view of the bulk from the worldline
• Out-of-Time-Order Correlation Functions for Unitary Minimal Models

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