Holographic Conformal Partial Waves as Gravitational Open Wilson Networks

TL;DR

This paper introduces a holographic method using open Wilson networks in gravitational theories to compute conformal partial waves in CFTs, successfully reproducing known results in 2D cases.

Contribution

It presents a novel holographic approach employing open Wilson networks to calculate conformal partial waves in any CFT decomposition.

Findings

Successfully computes global conformal blocks in 2D CFTs

Reproduces many known results in conformal partial wave calculations

Provides a new gauge-theoretic perspective on gravity in holography

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.