# From 4d Ambitwistor Strings to On Shell Diagrams and Back

## TL;DR

This paper explores the connection between 4d ambitwistor string theory and on-shell diagrams, deriving new formulas for scattering amplitudes in supersymmetric theories at tree and 1-loop levels.

## Contribution

It introduces novel Grassmannian integral formulas for tree-level amplitudes and new worldsheet formulas for 1-loop amplitudes in supersymmetric gauge and gravity theories.

## Key findings

- Derived new Grassmannian integral formulas for tree-level amplitudes.
- Obtained worldsheet formulas for 1-loop amplitudes with manifest supersymmetry.
- Established a refined scattering equations framework for loop calculations.

## Abstract

We investigate the relation between 4d ambitwistor string theory and on-shell diagrams for planar N=4 super-Yang-Mills and N=8 supergravity, and deduce several new results about their scattering amplitudes at tree-level and 1-loop. In particular, we derive new Grassmannian integral formulae for tree-level amplitudes and obtain new worldsheet formulae for 1-loop amplitudes which are manifestly supersymmetric and supported on scattering equations refined by MHV degree.