We consider correlation functions of single trace operators approaching the cusps of null polygons in a double-scaling limit where so-called cusp times $t_i^2=g^2\log x_{i-1,i}^2\log x_{i,i+1}^2$ 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 colors, including planar $\mathcal{N}=4$ SYM.

• Received 18 August 2022
• Accepted 28 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.221601

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Published by the American Physical Society