Applications of strong Szego limit theorem in AdS/CFT

Abstract: I will review a recent progress in computing four-point correlation functions of infinitely heavy half-BPS operators in planar N = 4 SYM. Taking advantage of integrability of the theory, these correlation functions can be constructed in terms of fundamental building blocks - the octagon form factors. We show that the octagon form factor can be expressed as a Fredholm determinant of an integrable Bessel operator and demonstrate that this representation is very efficient in finding its dependence on the ’t Hooft coupling and two cross ratios. At weak coupling, this yields a known series representation of the octagon in terms of ladder integrals. At strong coupling, we apply strong Szego limit theorem to develop a systematic expansion of the octagon in the inverse powers of the coupling constant and calculate accompanying expansion coefficients analytically.

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

London Integrability Journal Club

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