# Polylogarithms from the bound state S-matrix

## TL;DR

This paper explores the computation of higher-point functions in N=4 super Yang-Mills theory using a triangulation approach with hexagon tiles, focusing on the glueing process and its quantum corrections.

## Contribution

It introduces an algorithmic method to analyze the glueing process in n-point functions, aiming to generalize previous magnon exchange analyses.

## Key findings

- Quantum corrections are carried by the glueing process.
- Analysis of three-tile glueing via magnon exchange.
- Development of an integral representation approach for hypergeometric sums.

## Abstract

Higher-point functions of gauge invariant composite operators in N=4 super Yang-Mills theory can be computed via triangulation. The elementary tile in this process is the hexagon introduced for the evaluation of structure constants. A glueing procedure welding the tiles back together is needed to return to the original object. In this note we present work in progress on n-point functions of BPS operators. In this case, quantum corrections are entirely carried by the glueing procedure. The lowest non-elementary process is the glueing of three adjacent tiles by the exchange of two single magnons. This problem has been analysed before. With a view to resolving some conceptional questions and to generalising to higher processes we are trying to develop an algorithmic approach using the representation of hypergeometric sums as integrals over Euler kernels.