The Octagon as a Determinant

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 t...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Authors: Kostov, Ivan, Petkova, Valentina B, Serban, Didina
Format: Article
Language:English
Subjects:
Bosons
Computation
Fermions
Feynman diagrams
Form factors
Graphical representations
Mathematical analysis
Matrix methods
Operators (mathematics)
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1905.11467