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We study the semiclassical holographic correspondence between 2d CFT n-pointconformal blocks and massive particle configurations in the asymptotically AdS3space. On the boundary we use the heavy-light approximation in which case twoof primary operators are the background for the other (n-2) operatorsconsidered as fluctuations. In the bulk the particle dynamics can be reduced tothe hyperbolic time slice. Although lacking exact solutions we neverthelessshow that for any n the classical n-point conformal block is equal to thelength of the dual geodesic network connecting n-3 cubic vertices of worldlinesegments. To this end, both the bulk and boundary systems are reformulated aspotential vector fields. Gradients of the conformal block and geodesic lengthare given respectively by accessory parameters of the monodromy problem andparticle momenta of the on-shell worldline action represented as a function ofinsertion points. We show that the accessory parameters and particle momentaare constrained by two different algebraic equation systems which neverthelesshave the same roots thereby guaranteeing the correspondence.

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