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.

Published version

References in corpus (25)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• 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
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Entanglement Entropy in the O(N) model
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• Quantum Dimension as Entanglement Entropy in 2D CFTs
• Entanglement of Local Operators in large N CFTs
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange
• Notes on Quantum Entanglement of Local Operators
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• A Semidefinite Program Solver for the Conformal Bootstrap
• Charged Renyi entropies and holographic superconductors
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Thermalization after holographic bilocal quench
• Holographic duals of large-c torus conformal blocks
• Scattering effect on entanglement propagation in RCFTs
• Analytic continuation formulae for the BPZ conformal block
• Bootstrapping Pure Quantum Gravity in AdS3
• A view of the bulk from the worldline

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