Exact null octagon

Understand

We consider the so-called simplest correlation function of four infinitely heavy half-BPS operators in planar N=4 SYM in the limit when the operators are light-like separated in a sequential manner.

• We find a closed-form expression for the correlation function in this limit as a function of the 't Hooft coupling and residual cross ratios.
• Our analysis heavily relies on the factorization of the correlation function into the product of null octagons and on the recently established determinant representation for the latter.
• We show that the null octagon is given by a Fredholm determinant of a certain integral operator which has a striking similarity to those previously encountered in the study of two-point correlation functions in exactly solvable models at finite temperature and of level spacing distributions for random matrices.