Holographic Conformal Partial Waves as Gravitational Open Wilson Networks

TL;DR

This work presents a holographic framework that computes conformal partial waves and global conformal blocks of a CFT via open Wilson network operators in Euclidean AdS gravity, formulated in the Hilbert-Palatini (BF-type) approach. By constructing boundary-anchored OWN in the sl(2,R)⊕sl(2,R) gauge theory (and projecting onto twisted diagonal so(3) representations), the authors show that the semiclassical bulk evaluation reproduces the correct Ward identities and Casimir equations for boundary correlators. They explicitly derive 2-, 3-, 4-, and 5-point global blocks in 2d CFTs, recovering known coordinate dependences and hypergeometric structures, thus establishing a bulk, gauge-theoretic realization of conformal blocks. The results underscore the kinematic, symmetry-determined nature of blocks and set the stage for extensions to Virasoro blocks, higher-spin theories, and quantum corrections.

Abstract

We propose a method to holographically compute the conformal partial waves in any decomposition of correlation functions of primary operators in conformal field theories using open Wilson network operators in the holographic gravitational dual. The Wilson operators are the gravitational ones where gravity is written as a gauge theory in the first order Hilbert-Palatini formalism. We apply this method to compute the global conformal blocks and partial waves in 2d CFTs reproducing many of the known results.