The octagon as a determinant

• Published in: The journal of high energy physics Vol. 2019; no. 11; pp. 1 - 27
• Main Authors: Kostov, Ivan, Petkova, Valentina B., Serban, Didina
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2019; Springer Nature B.V; Springer; SpringerOpen
• Subjects: AdS-CFT Correspondence; Bosons; Classical and Quantum Gravitation; Computation; Elementary Particles; Fermions; Feynman diagrams; Form factors; Fourier transforms; Graphical representations; High energy physics; High Energy Physics - Theory; Integrable Field Theories; Integrals; Mathematical analysis; Matrices (mathematics); Matrix methods; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; AdS-CFT Correspondence; Integrable Field Theories; operator: BPS; n-point function: 4; nonperturbative; rapidity; weak coupling; form factor; Feynman graph; determinant
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP11(2019)178

A bstract The computation of a certain class of four-point functions of heavily charged BPS operators boils down to the computation of a special form factor — the octagon. In this paper, which is an extended version of the short note [1], we derive a non-perturbative formula for the square of the octagon as the determinant of a semi-infinite skew-symmetric matrix. We show that perturbatively in the weak coupling limit the octagon is given by a determinant constructed from the polylogarithms evaluating ladder Feynman graphs. We also give a simple operator representation of the octagon in terms of a vacuum expectation value of massless free bosons or fermions living in the rapidity plane.