Scalar Blocks as Gravitational Wilson Networks

TL;DR

This paper advances the holographic computation of conformal partial waves in CFTs using gravitational Wilson networks, introducing OPE modules and deriving new recursion relations for scalar partial waves across dimensions.

Contribution

It extends the Wilson network approach to compute four-point scalar partial waves in any dimension, introducing OPE modules and new recursion relations.

Findings

Scalar partial waves expressed with Gegenbauer polynomials

Simplified proof of recursion relations for even dimensions

Extension of methods to odd-dimensional CFTs

Abstract

In this paper we continue to develop further our prescription [arXiv:1602.02962] to holographically compute the conformal partial waves of CFT correlation functions using the gravitational open Wilson network operators in the bulk. In particular, we demonstrate how to implement it to compute four-point scalar partial waves in general dimension. In the process we introduce the concept of OPE modules, that helps us simplify the computations. Our result for scalar partial waves is naturally given in terms of the Gegenbauer polynomials. We also provide a simpler proof of a previously known recursion relation for the even dimensional CFT partial waves, which naturally leads us to an odd dimensional counterpart.