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

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 expresses 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, and the latter expresses tree amplitudes in nonlinear 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.