Stampedes II: Null Polygons in Conformal Gauge Theory

TL;DR

This paper investigates correlation functions of operators near null polygon cusps in conformal gauge theories, deriving coupled Toda-type PDEs that uniquely determine these correlators in a specific double-scaling limit.

Contribution

It introduces a novel approach using stampedes, symbols, and educated guesses to derive coupled Toda-type PDEs for null polygon correlators in conformal gauge theories.

Findings

Correlators are fixed by coupled lattice PDEs of Toda type.

Results apply to large N conformal gauge theories, including planar  SYM.

The approach reveals new features of cusp-related correlators.

Abstract

We consider correlation functions of single trace operators approaching the cusps of null polygons in a double-scaling limit where so-called $\textit{cusp times}$ $t_i^2 = g^2 \log x_{i-1,i}^2\log x_{i,i+1}^2$ are held fixed and the t'Hooft coupling is small. With the help of stampedes, symbols and educated guesses, we find that any such correlator can be uniquely fixed through a set of coupled lattice PDEs of Toda type with several intriguing novel features. These results hold for most conformal gauge theories with a large number of colours, including planar $\mathcal{N}=4$ SYM.