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.

arXiv comment41 pages, 10 figures. (Published version; typos corrected and references added.)

References in corpus (62)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Bounding scalar operator dimensions in 4D CFT
• Holography from Conformal Field Theory
• Solving the 3D Ising Model with the Conformal Bootstrap
• Conformal Partial Waves and the Operator Product Expansion
• Writing CFT correlation functions as AdS scattering amplitudes
• Entanglement Renyi entropies in holographic theories
• 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
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Entanglement Entropy at Large Central Charge
• Emergent Spacetime and Holographic CFTs
• Correlation functions for M^N/S_N orbifolds
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• Quantum Entanglement of Local Operators in Conformal Field Theories
• Holographic entanglement beyond classical gravity
• 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
• From Free Fields to $AdS$
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Central Charge Bounds in 4D Conformal Field Theory
• Holographic three-point functions of semiclassical states
• Classical Conformal Blocks and Painleve VI
• Conformal Bootstrap, Universality and Gravitational Scattering
• Mutual information after a local quench in conformal field theory
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Time evolution of entanglement entropy from a pulse
• From Free Fields to $AdS$ -- III
• Virasoro conformal blocks in closed form
• Higher Spin Entanglement and W_N Conformal Blocks
• Notes on Quantum Entanglement of Local Operators
• More Holography from Conformal Field Theory
• Hawking from Catalan
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Scrambling time from local perturbations of the eternal BTZ black hole
• Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
• From Free Fields to AdS -- II
• String Universality for Permutation Orbifolds
• Classical conformal blocks via AdS/CFT correspondence
• 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
• Entanglement constant for conformal families
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Emergent space-time and the supersymmetric index
• Looking for a bulk point
• Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling
• On the monodromy problem for the four-punctured sphere
• AdS plane waves, entanglement and mutual information
• Classical conformal blocks
• Accessory parameters for Liouville theory on the torus
• The Epsilon-Expansion from Conformal Field Theory
• Conformal Blocks Beyond the Semi-Classical Limit

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• Probing thermality beyond the diagonal
• Relative entropy of excited states in two dimensional conformal field theories
• Entanglement negativity, Holography and Black holes
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• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• On the Virasoro six-point identity block and chaos
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• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
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