Abstract
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.
Highlights
Question arises: why these theories? Imbued with symmetries of disparate origin and character, these theories do not obviously conform to any cohesive organizing principle that would place them on equal footing in the eyes of the S-matrix
Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones
A trivial corollary of these unifying relations is the universality of the KLT, BCJ, and CHY constructions. Because these structures generalize to arbitrary spacetime dimension, the associated scattering amplitudes can be represented as functions of Lorentz invariant products of momentum and polarization vectors — so transmutation applies
Summary
The purpose of a transmutation operator T is to convert a gauge invariant object A into a new gauge invariant object T · A. A physical scattering amplitude of massless particles is welldefined on the support of the on-shell conditions, pipi = piei = 0, and momentum conservation, i pi = 0. To preserve the on-shell conditions, we define the physical scattering amplitude. Pv · T · A = T · Pv · A = 0, i.e. the transmuted amplitude conserves momentum A physical scattering amplitude should be gauge invariant. To incorporate this constraint we define a differential operator corresponding to the Ward identity on particle i, Wi ≡ piv ∂vei. Wi is itself momentum-conserving and gauge invariant.
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