Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles

TL;DR

This paper introduces universal expansions of tree-level scattering amplitudes for gravitons, gluons, and Goldstone particles, revealing their relations across different theories and deriving from gauge invariance principles.

Contribution

It presents new universal expansion formulas for scattering amplitudes in gravity, gauge, and effective field theories, connecting them through gauge invariance and dimension reduction.

Findings

Expresses gravity and gauge amplitudes as linear combinations of simpler amplitudes.

Derives expansions for non-linear sigma model, Born-Infeld, and Galileon theories.

Links gauge-theory expansions to effective field theories via dimension reduction.

Abstract

Tree-level scattering amplitudes for gravitons, gluons and Goldstone particles in any dimensions are strongly constrained by basic principles, and they are intimately related to each other via various relations. We study two types of "universal expansions" with respect to gauge bosons and Goldstone bosons: the former express tree amplitudes in Einstein gravity (Yang-Mills) as linear combinations of single-trace Einstein-Yang-Mills (Yang-Mills-$\phi^3$) amplitudes with coefficients given by Lorentz products of polarizations and momenta; the latter express tree amplitudes in non-linear sigma model, (Dirac-)Born-Infeld and a special Galileon theory, as linear combinations of single-trace mixed amplitudes with particles of lower "degree of Adler's zero" and coefficients given by products of Mandelstam variables. We trace the origin of gauge-theory expansions to the powerful uniqueness theorem based on gauge invariance, and expansions in effective field theories can be derived from gauge-theory ones via a special dimension reduction.