Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin

TL;DR

This paper explores the conformal bootstrap for higher-point functions in non-abelian gauge theories, constraining OPE data near null polygon cusps, and fully determining them in N=4 SYM via Wilson loop duality.

Contribution

It introduces a bootstrap approach for n>4 point functions in gauge theories, constraining OPE constants and connecting to Wilson loop duality in N=4 SYM.

Findings

Strong constraints on OPE structure constants for large spin operators.

Complete determination of OPE data in N=4 SYM via Wilson loop duality.

Extension of bootstrap methods to null polygon configurations.

Abstract

We initiate an exploration of the conformal bootstrap for $n>4$ point correlation functions. Here we bootstrap correlation functions of the lightest scalar gauge invariant operators in planar non-abelian conformal gauge theories as their locations approach the cusps of a null polygon. For that we consider consistency of the OPE in the so-called snowflake channel with respect to cyclicity transformations which leave the null configuration invariant. For general non-abelian gauge theories this allows us to strongly constrain the OPE structure constants of up to three large spin $J_j$ operators (and large polarization quantum number $l_{j}$) to all loop orders. In $ \mathcal{N}=4$ we fix them completely through the duality to null polygonal Wilson loops and the recent origin limit of the hexagon explored by Basso, Dixon and Papathanasiou.