# Determinant Formula for the Octagon Form Factor in $N=4$ Supersymmetric Yang-Mills Theory

Kostov, Ivan (Institut de Physique Théorique, DRF-INP 3681, C.E.A.-Saclay, F-91191 Gif-sur-Yvette, France) ; Petkova, Valentina B. (Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria) ; Serban, Didina (Institut de Physique Théorique, DRF-INP 3681, C.E.A.-Saclay, F-91191 Gif-sur-Yvette, France)

12 June 2019

Abstract: We present a closed expression for the octagon form factor which appears as a building block in a class of four-point correlation functions in $N=4$ supersymmetric Yang-Mills theory considered recently by Coronado. The octagon form factor is expressed, to all loop orders, as the determinant of a semi-infinite matrix. We find that perturbatively at weak coupling the entries of this matrix are linear combinations of ladder functions with simple rational coefficients.

Published in: Physical Review Letters 122 (2019)