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Exact null octagon

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arxiv 1907.13131 v2 pith:IYIAUE47 submitted 2019-07-30 hep-th

A.V. Belitsky , G.P. Korchemsky This is my paper · ORCID
classification hep-th
keywords correlationfunctionnulloctagondeterminantexactlylimitoperators
verification ladder T0 review T1 audit T2 compute T3 formal
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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. This allows us to compute the null octagon exactly by employing a method of differential equations.

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Cited by 5 Pith papers

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    A general two-loop formula is obtained for all n-point 10d null polygon correlators in planar N=4 SYM, expressed in a conformal-integral basis and verified numerically at 11 points.

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    hep-th 2026-07 conditional novelty 6.0 of 10

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