Higher-point conformal blocks and entanglement entropy in heavy states

Abstract

We consider conformal blocks of two heavy operators and an arbitrary number of light operators in a (1+1)-d CFT with large central charge. Using the monodromy method, these higher-point conformal blocks are shown to factorize into products of 4-point conformal blocks in the heavy-light limit for a class of OPE channels. This result is reproduced by considering suitable worldline configurations in the bulk conical defect geometry. We apply the CFT results to calculate the entanglement entropy of an arbitrary number of disjoint intervals for heavy states. The corresponding holographic entanglement entropy calculated via the minimal area prescription precisely matches these results from CFT. Along the way, we briefly illustrate the relation of these conformal blocks to Riemann surfaces and their associated moduli space.

41 pages, 10 figures. (Published version; typos corrected and references added.)

References in corpus (23)

• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Entanglement Entropy at Large Central Charge
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• On three-point correlation functions in the gauge/gravity duality
• Quantum Dimension as Entanglement Entropy in 2D CFTs
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Central Charge Bounds in 4D Conformal Field Theory
• Notes on Quantum Entanglement of Local Operators
• String Universality for Permutation Orbifolds
• HHL correlators, orbit averaging and form factors
• From global to heavy-light: 5-point conformal blocks
• Permutation orbifolds and holography
• Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Emergent space-time and the supersymmetric index
• AdS plane waves, entanglement and mutual information
• Classical conformal blocks
• The Epsilon-Expansion from Conformal Field Theory
• Conformal Blocks Beyond the Semi-Classical Limit

Cited by in corpus (57)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Holographic Pseudo Entropy
• Black Hole Collapse in the 1/c Expansion
• Spinning Witten Diagrams
• Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
• Probing thermality beyond the diagonal
• Relative entropy of excited states in two dimensional conformal field theories
• Entanglement negativity, Holography and Black holes
• Universal Lowest-Twist in CFTs from Holography
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Holographic dual of the five-point conformal block
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Phases of scrambling in eigenstates
• Towards Entanglement of Purification for Conformal Field Theories
• Holographic conformal blocks from interacting Wilson lines
• Holographic interpretation of 1-point toroidal block in the semiclassical limit
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• State Dependence of Krylov Complexity in $2d$ CFTs
• A slow review of the AGT correspondence
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• On the Virasoro six-point identity block and chaos
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Holographic duals of large-c torus conformal blocks
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Six-point functions and collisions in the black hole interior
• Various semiclassical limits of torus conformal blocks
• Entanglement Entropy after Double-Excitation as Interaction Measure
• Holographic variables for CFT${}_2$ conformal blocks with heavy operators
• Entanglement entropy after selective measurements in quantum chains
• More on Wilson toroidal networks and torus blocks
• Reflected entropy in BCFTs on a black hole background
• Large-c superconformal torus blocks
• Geodesic description of Heavy-Light Virasoro blocks
• On the universality of late-time correlators in semi-classical 2d CFTs
• Semiclassical torus blocks in the t-channel
• Four-point conformal blocks with three heavy background operators
• Correspondence between Entanglement Growth and Probability Distribution of Quasi-Particles
• Holographic relations for OPE blocks in excited states
• Holographic Reflected Entropy and Islands in Interface CFTs
• A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• Aspects of Holography in Conical $Ad{S}_3$
• Chaos bound in Bershadsky-Polyakov theory
• Solving Heun's equation using conformal blocks
• Wilson lines construction of ${\mathfrak{sl}}_3$ toroidal conformal blocks
• Sine-Gordon Theory : Entanglement entropy and holography
• Large-$c$ conformal $(n\le 6)$-point blocks with superlight weights and holographic Steiner trees
• Toward Null State Equations in $d>2$
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models
• Example of the $4$-pt non-vacuum ${\mathcal{W}}_3$ classical block
• Reparametrization mode Ward Identities and chaos in higher-pt. correlators in CFT${}_2$
• Generalized monodromy method in gauge/gravity duality
• Quantum Information Approaches to Quantum Gravity
• Holographic Reflected Entropy: Islands and Defect Phases