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Published February 2018 | Published + Submitted
Journal Article Open

Unifying Relations for Scattering Amplitudes


We derive new amplitudes relations revealing a hidden unity among a wideranging variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. Transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.

Additional Information

© 2018 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: June 5, 2017; Revised: November 14, 2017; Accepted: February 8, 2018; Published: February 15, 2018. We would like to thank Henrik Johansson and Ellis Yuan for discussions which inspired this work, as well as Bo Feng, Song He, Yu-tin Huang, Jan Plefka, Oliver Schlotterer, Stephen Stieberger, and Wadim Wormsbecher for helpful discussions. CHS and CW are grateful to the KITP, Santa Barbara, for hospitality during the final stages of this work. CC is supported by a Sloan Research Fellowship and CC, CHS, and CW are supported in part by a DOE Early Career Award under Grant No. DE-SC0010255 and by the NSF under Grant No. NSF PHY-1125915.

Attached Files

Published - 10.1007_2FJHEP02_2018_095.pdf

Submitted - 1705.03025.pdf


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August 19, 2023
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