Holographic conformal blocks from interacting Wilson lines
Mert Besken, Ashwin Hegde, Eliot Hijano, Per Kraus
TL;DR
This work introduces a bulk AdS$_3$/CFT$_2$ prescription in which conformal blocks and correlators are computed holographically from Wilson lines merging at a bulk vertex, producing exact matches to global blocks, heavy-light Virasoro blocks, and ${\cal W}_N$ blocks in the large central charge limit. The method relies on a master expression that reduces correlators to SL$(N)$ representation theory via singlet construction, enabling explicit SL$(2)$, SL$(3)$ and general SL$(N)$ computations, including crossing symmetry constraints. It yields concrete holomorphic blocks for several channels, and shows how heavy operators can be incorporated through bulk backreaction (conical defects) to reproduce heavy-light blocks. The approach offers a transparent, representation-theoretic route to conformal blocks at large $c$, with analytic continuation in $N$ connecting to ${\cal W}_{\infty}(\lambda)$ and potential links to Prokushkin–Vasiliev theory for future quantum corrections.
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.