Many-point classical conformal blocks and geodesic networks on the hyperbolic plane

Abstract

We study the semiclassical holographic correspondence between 2d CFT n-point conformal blocks and massive particle configurations in the asymptotically AdS3 space. On the boundary we use the heavy-light approximation in which case two of primary operators are the background for the other (n-2) operators considered as fluctuations. In the bulk the particle dynamics can be reduced to the hyperbolic time slice. Although lacking exact solutions we nevertheless show that for any n the classical n-point conformal block is equal to the length of the dual geodesic network connecting n-3 cubic vertices of worldline segments. To this end, both the bulk and boundary systems are reformulated as potential vector fields. Gradients of the conformal block and geodesic length are given respectively by accessory parameters of the monodromy problem and particle momenta of the on-shell worldline action represented as a function of insertion points. We show that the accessory parameters and particle momenta are constrained by two different algebraic equation systems which nevertheless have the same roots thereby guaranteeing the correspondence.

arXiv comment29 pages

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• Holographic dual of the five-point conformal block
• Entanglement negativity at large central charge
• Witten Diagrams for Torus Conformal Blocks
• On the Virasoro six-point identity block and chaos
• Thermalization after holographic bilocal quench
• 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
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• Bootstrapping closed string field theory
• Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits
• Various semiclassical limits of torus conformal blocks
• Holographic variables for CFT${}_2$ conformal blocks with heavy operators
• Anomalous dimensions from quantum Wilson lines
• Large-c superconformal torus blocks
• More on Wilson toroidal networks and torus blocks
• Geodesic description of Heavy-Light Virasoro blocks
• Four-point conformal blocks with three heavy background operators
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• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models
• Reparametrization mode Ward Identities and chaos in higher-pt. correlators in CFT${}_2$
• Generalized monodromy method in gauge/gravity duality