# Four dimensional ambitwistor strings and form factors of local and Wilson line operators

## TL;DR

This paper develops a four-dimensional ambitwistor string framework to compute form factors of local and Wilson line operators in N=4 SYM, reproducing known Grassmannian representations and deriving new scattering equations.

## Contribution

It introduces explicit string composite operators for stress-tensor and Wilson line operators, connecting ambitwistor strings with form factors and on-shell amplitudes.

## Key findings

- Tree-level correlation functions match Grassmannian integral representations.
- Derived four-dimensional scattering equations for form factors.
- Established a gluing procedure linking operator form factors to on-shell amplitudes.

## Abstract

We consider the description of form factors of local and Wilson line operators (reggeon amplitudes) in N=4 SYM within the framework of four dimensional ambitwistor string theory. We present the explicit expressions for string composite operators corresponding to stress-tensor operator supermultiplet and Wilson line operator insertion. It is shown, that corresponding tree-level string correlation functions correctly reproduce previously obtained Grassmannian integral representations. As by product we derive four dimensional tree-level scattering equations representations for the mentioned form factors and formulate a simple gluing procedure used to relate operator form factors with on-shell amplitudes.