# Unifying Relations for Scattering Amplitudes

## TL;DR

This paper introduces a unifying framework using Lorentz invariant differential operators to relate and generate scattering amplitudes across a wide range of theories, revealing deep connections and simplifying complex relations.

## Contribution

It develops a set of transmutation operators that connect diverse theories' amplitudes, unifying their structures and deriving new relations among them.

## Key findings

- Generated all amplitudes of several theories from gravity amplitudes.
- Revealed that key amplitude relations are inherited through transmutation.
- Derived new soft theorems for scalar theories.

## Abstract

We derive new amplitudes relations revealing a hidden unity among wide-ranging theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. Transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.