# Structure constants of operators on the Wilson loop from integrability

## TL;DR

This paper investigates the structure constants of operators on the Wilson loop in N=4 super Yang-Mills theory, using integrability techniques to compute and interpret these constants at tree level and proposing a conjecture for finite coupling.

## Contribution

It introduces a novel approach to compute structure constants on the Wilson loop via open spin chains and hexagon form factors, extending integrability methods to this context.

## Key findings

- Computed structure constants at tree level in the SU(2) sector.
- Interpreted results as summation over magnon momentum sign changes.
- Proposed a conjecture for finite coupling based on holographic duality.

## Abstract

We study structure constants of local operators inserted on the Wilson loop in ${\cal N}=4$ super Yang-Mills theory. We compute the structure constants in the SU(2) sector at tree level using the correspondence between operators on the Wilson loop and the open spin chain. The results are interpreted as the summation over all possible ways of changing the signs of magnon momenta in the hexagon form factors. This is consistent with a holographic description of the correlator as the cubic open string vertex, which consists of one hexagonal patch and three boundaries. We then conjecture that a similar expression should hold also at finite coupling.