Null octagon from Deift-Zhou steepest descent

A. V. Belitsky

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arXiv · 2012.10446

Null octagon from Deift-Zhou steepest descent

A. V. Belitsky

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Abstract

A special class of four-point correlation functions in the maximally supersymmetric Yang-Mills theory is given by the square of the Fredholm determinant of a generalized Bessel kernel. In this note, we re-express its logarithmic derivatives in terms of a two-dimensional Riemann-Hilbert problem. We solve the latter in the null limit making use of the Deift-Zhou steepest descent. We reproduce the exact octagonal anomalous dimension in 't Hooft coupling and provide its novel formulation as a convolution of the non-linear quasiclassical phase with the Fermi distribution in the limit of the infinite chemical potential.

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hep-th math-ph math.MP nlin.SI

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A. V. Belitsky. 2020-12-18. Null octagon from Deift-Zhou steepest descent. https://arxiv.org/abs/2012.10446

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