Note on differential operators, CHY integrands, and unifying relations for amplitudes

TL;DR

This paper unifies various amplitude theories within the CHY framework by relating differential operators to integrands, connecting multiple theories including gravity, Yang-Mills, and scalar models in a comprehensive web.

Contribution

It establishes a systematic relation between differential operator approach and CHY integrands, unifying multiple theories' amplitudes in a single framework.

Findings

Unified web for amplitudes of various theories established.

Relation between differential operators and CHY integrands demonstrated.

Includes a wide range of theories from gravity to scalar models.

Abstract

An elegant unified web for amplitudes of various theories was given by Cachazo, He and Yuan in the CHY framework a few years ago. Recently, similar web has also been constructed by Cheung, Shen and Wen, which relies on a set of differential operators. In this note, by acting these differential operators on CHY-integrands systematically, we have established the relation between these two approaches. Thus, amplitudes for all theories which have CHY representations, include gravity theory, Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory and its extension, bi-adjoint scalar theory, $\phi^4$ theory, non-linear sigma model, as well as special Galileon theory, have been included in the unified web rooted from gravity theory.