Abstract
The various formulations of scattering amplitudes presented in recent years have underlined a hidden unity among very different theories. The KLT and BCJ relations, together with the CHY formulation, connect the S-matrices of a wide range of theories: the transmutation operators, recently proposed by Cheung, Shen and Wen, provide an account for these similarities. In this note we use the transmutation operators to link the various CHY integrands at tree-level. Starting from gravity, we generate the integrands for Yang-Mills, biadjoint scalar, Einstein-Maxwell, Yang-Mills scalar, Born-Infeld, Dirac-Born-Infeld, non-linear sigma model and special Galileon theories, as well as for their extensions. We also commence the study of the CHY-like formulae at loop level.
Highlights
We collect some details on these operators, which will be useful in the following
We summarize the various integrands which will appear in this paper [4, 5]
The similarity between tree-level and one-loop amplitudes finds its reason in the Feynman tree theorem and it is realised in the ambitwistor string context by the so-called gluing operator [10]
Summary
A set of first-order differential operator has been proposed [6], which transmutes amplitudes of various massless theories in arbitrary spacetime dimensions into each other. These two-point operators reduce the spin of particles i and j by one, placing them within a new color trace structure: Tij = ∂eiej They transmute gravitons into photons, gluons into biadjoint scalars, and BI photons into DBI scalars. These operators reduce the spin of particle j by one and insert it within an already existing trace structure between particles i and k: Tijk = ∂piej − ∂pkej They transmute gravitons into gluons, gluons into biadjoint scalars, and BI photons into pions. Let us consider a color-ordered Yang-Mills amplitude of n gluons and apply, first, the trace operator Tik. Particles i and k are transmuted to biadjoint scalars and placed inside a trace structure with respect to their dual color. (2.12) generates the extended versions of BI, NLSM and SG
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