Light-Cone Bootstrap of Higher Point Functions and Wilson Loop Duality

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 Jj operators (and large polarization quantum number lj) to all loop orders. In 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.