Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM

TL;DR

This paper derives a determinant formula for the octagon form factor in N=4 SYM, providing an all-loop expression and detailed weak coupling expansion, advancing understanding of correlation functions in this theory.

Contribution

It introduces a determinant representation of the octagon form factor valid at all loops, with explicit weak coupling expansion details.

Findings

Determinant formula for the octagon form factor derived.

Explicit weak coupling expansion provided.

Entries of the matrix involve ladder functions with rational coefficients.

Abstract

We compute to all loop orders correlation function of four heavy BPS operators in $\mathcal{N}$= 4 SYM with special polarisations considered recently by Frank Coronado. Our main result is an expression for the octagon form factor as determinant of a semi-infinite matrix. We find that at weak coupling the entries of this matrix are linear combinations of ladder functions with simple rational coefficients and give the full perturbative expansion of the octagon.