Null Polygons in Conformal Gauge Theory

We consider correlation functions of single trace operators approaching the cusps of null polygons in a double-scaling limit where so-called cusp times t(i)(2) = g(2) log x(i-1,i)(2) logx(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 colors, including planar N = 4 SYM.

Automated summary

We study correlation functions of single trace operators approaching the cusps of null polygons in a double-scaling limit. We find that these correlators can be uniquely fixed through a set of coupled lattice PDEs of Toda type. These results are applicable to most conformal gauge theories.