Null Polygons in Conformal Gauge Theory

Abstract

We consider correlation functions of single trace operators approaching the cusps of null polygons in a double-scaling limit where so-called cusp times ti2=g2logxi-1,i2logxi,i+12 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 colors, including planar N=4 SYM.