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

• Published in: The journal of high energy physics Vol. 2018; no. 9; pp. 1 - 20
• Main Authors: Zhou, Kang, Feng, Bo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-09-2018; Springer Nature B.V; SpringerOpen
• Subjects: Amplitudes; Born-Infeld theory; Classical and Quantum Gravitation; Differential equations; Elementary Particles; Field theory; Gauge Symmetry; Gravitation; High energy physics; Operators; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; String Theory; Webs; Yang-Mills theory; Gauge Symmetry; Scattering Amplitudes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2018)160

A
bstract
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,
ϕ
4
theory, non-linear sigma model, as well as special Galileon theory, have been included in the unified web rooted from gravity theory.