Séminaire de Physique ThéoriqueClassical conformal blocks and the Steiner tree problem
Konstantin Alkalaev (Institut de physique Lebedev, Moscou)
Monday 04 February 2019 13:00 - Tours - Salle 1180 (Bât E2)
We discuss the Steiner tree problem in hyperbolic geometry in the context of the AdS/CFT duality between large-c conformal blocks on the boundary and particle motions in the bulk. The Steiner trees are weighted graphs on the Poincare disk with a number of endpoints and trivalent vertices connected to each other by edges in such a way that an overall length is a minimum. We specify a particular class of Steiner trees that we call holographic. Their characteristic property is that a holographic Steiner tree with N endpoints can be inscribed into an N-gon with N−1 ideal vertices. The holographic Steiner trees are dual to large-c conformal blocks. Particular examples of N=2,3,4 Steiner trees as well as their dual conformal blocks are explicitly calculated. We discuss the geometric properties of the holographic Steiner trees and their realization in CFT terms. It is shown that connectivity and cuts of the Steiner trees encode the factorization properties of large-c conformal blocks.