English

The Octagon as a Determinant

High Energy Physics - Theory 2020-01-29 v3

Abstract

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.

Keywords

Cite

@article{arxiv.1905.11467,
  title  = {The Octagon as a Determinant},
  author = {Ivan Kostov and Valentina B. Petkova and Didina Serban},
  journal= {arXiv preprint arXiv:1905.11467},
  year   = {2020}
}

Comments

22 pages, 1 figure, small typos corrected

R2 v1 2026-06-23T09:27:37.707Z