Unifying relations for scattering amplitudes

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.

The B-field soft theorem and its unification with the graviton and dilaton

“…(1.9). This universal expression is a step towards understanding the interplay between the infrared behaviors of Yang-Mills theory and gravity as Yang-Mills squared theory [19].…”

“…It is well known from string theory that amplitudes of this theory can be described in a unified way, which we in short will describe. Nevertheless, while it is known that the graviton and dilaton obey soft theorems, a soft theorem for the two form is still missing [19,20]. The aim of this paper is to fill this gap, and to derive a unified soft theorem valid universally for the graviton, dilaton and the two-form.…”

Monopoles, shockwaves and the classical double copy

“…refs. [47,[98][99][100] for further details. 5 Recently, the known electromagnetic duality relating electric and magnetic charges has been explored from a double copy point of view [83,107,108].…”

Vector Effective Field Theories from Soft Limits

“…These theories exhibit maximally strong soft behavior, exposing them as the EFT analogs of gauge theory and gravity [4,5]. These scalar EFTs appear in a variety of disparate contexts, e.g., the Cachazo-He-Yuan formalism [6][7][8], certain world sheet models [9], the Bern-CarrascoJohansson double-copy construction [10,11], and the web of unifying relations for massless theories [12,13].…”

“…Any tree amplitude of vectors is a polynomial in ðe i · e j Þ, with coefficients that depend on ðe i · p j Þ and ðp i · p j Þ. The reduced amplitudes are obtained from the original expression by applying derivatives with respect to ∂=∂ðe i · e j Þ [12]. Moreover, derivatives of the amplitude fix the original amplitude up to a "constant," which depends only on ðe i · p j Þ and ðp i · p j Þ.…”