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Note on differential operators, CHY integrands, and unifying relations for amplitudes
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, theory, non-linear sigma model, as well as special
Galileon theory, have been included in the unified web rooted from gravity
theory.Comment: 20 page
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