# String amplitudes from field-theory amplitudes and vice versa

## TL;DR

This paper develops a method to relate massless string amplitudes to field-theory amplitudes using integration-by-parts reduction and CHY formulas, revealing a double copy structure and deriving new integrands for specific theories.

## Contribution

It introduces a generic IBP reduction technique for string correlators and connects string amplitudes to field-theory via CHY formulas, including new integrands for certain gauge theories.

## Key findings

- String amplitudes are the double copy of field-theory amplitudes and specific integrals.
- A universal IBP reduction applies to any rational correlator with correct SL(2) weight.
- Derived a closed-form CHY integrand for the $(DF)^2+YM+ ext{phi}^3$ theory.

## Abstract

We present an integration-by-parts reduction of any massless tree-level string correlator to an equivalence class of logarithmic functions, which can be used to define a field-theory amplitude via a Cachazo-He-Yuan (CHY) formula. The string amplitude is then shown to be the double copy of the field-theory one and a special disk/sphere integral. The construction is generic as it applies to any correlator that is a rational function of correct SL(2) weight. By applying the reduction to open bosonic/heterotic strings, we get a closed-form CHY integrand for the $(DF)^2+\text{YM}+\phi^3$ theory.