Classical conformal blocks via AdS/CFT correspondence

TL;DR

This paper advances the holographic interpretation of classical conformal blocks in AdS3 by explicitly describing bulk configurations with multiple particles and validating the approach through detailed five-point case analysis.

Contribution

It introduces a bulk worldline configuration for n-point blocks with heavy and light fields and confirms the correspondence through explicit five-point calculations.

Findings

Bulk configuration with particles in conical defect background described.

Exact match between 5-point conformal block and bulk worldline action.

Perturbative approach treats 5-point case as deformation of 4-point case.

Abstract

We continue to develop the holographic interpretation of classical conformal blocks in terms of particles propagating in an asymptotically $AdS_3$ geometry. We study $n$-point block with two heavy and $n-2$ light fields. Using the worldline approach we propose and explicitly describe the corresponding bulk configuration, which consists of $n-3$ particles propagating in the conical defect background produced by the heavy fields. We test this general picture in the case of five points. Using the special combinatorial representation of the Virasoro conformal block we compute $5$-point classical block and find the exact correspondence with the bulk worldline action. In particular, the bulk analysis relies upon the special perturbative procedure which treats the $5$-point case as a deformation of the $4$-pt case.