TL;DR
This paper demonstrates how transmutation operators can connect various tree-level CHY integrands across multiple theories, revealing a unified structure and extending the approach to loop-level formulations.
Contribution
It introduces a method to relate different CHY integrands using transmutation operators, unifying multiple theories at tree-level and initiating exploration at loop-level.
Findings
Generated integrands for various theories from gravity using transmutation
Established connections among different theories' CHY formulations
Initiated study of CHY-like formulas at loop level
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.
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