Holographic conformal blocks from interacting Wilson lines

TL;DR

This paper introduces a holographic method using Wilson lines to compute conformal blocks and correlation functions in AdS3, successfully reproducing known blocks and extending to higher spin theories with explicit calculations.

Contribution

It provides a new, straightforward prescription for holographically computing conformal blocks using Wilson lines merging at a bulk vertex, applicable to various theories including higher spin cases.

Findings

Reproduces global conformal blocks holographically

Derives heavy-light Virasoro blocks using Wilson lines

Establishes correspondence with ${ m W}_N$ conformal blocks

Abstract

We present a simple prescription for computing conformal blocks and correlation functions holographically in AdS$_3$ in terms of Wilson lines merging at a bulk vertex. This is shown to reproduce global conformal blocks and heavy-light Virasoro blocks. In the case of higher spin theories the space of vertices is in one-to-one correspondence with the space of ${\cal W}_N$ conformal blocks, and we show how the latter are obtained by explicit computations.