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

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, ${\varphi }^4$ theory, non-linear sigma model, as well as special Galileon theory, have been included in the unified web rooted from gravity theory.

arXiv comment20 pages

References in corpus (13)

• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Extensions of Theories from Soft Limits
• Unifying Relations for Scattering Amplitudes
• New Relations for Einstein-Yang-Mills Amplitudes
• Expansion of Einstein-Yang-Mills Amplitude
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Expansion of All Multitrace Tree Level EYM Amplitudes
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation

Cited by in corpus (19)

• Radiation of scalar modes and the classical double copy
• Shift symmetries, soft limits, and the double copy beyond leading order
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• Transmuting CHY formulae
• Unified web for expansions of amplitudes
• The Infrared Structure of Exceptional Scalar Theories
• A Type of Unifying Relation in (A)dS Spacetime
• Matter Couplings and Equivalence Principles for Soft Scalars
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Expansion of tree amplitudes for EM and other theories
• On differential operators and unifying relations for $1$-loop Feynman integrands
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Transmuting off-shell CHY integrals in the double-cover framework
• Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• CHY Theory for Several Fields
• The off-shell expansion relation of the Yang-Mills scalar theory