Graviton and gluon scattering from first principles

TL;DR

This work derives graviton and gluon scattering amplitudes from minimal, first-principles constraints—Poincaré invariance, gauge symmetry, unitarity—by treating amplitudes as linear combinations of Lorentz-invariant contraction blocks and solving the resulting on-shell linear system. It shows that many gravity-gauge relations (KLT-type) arise from linearised diffeomorphism invariance and that products of gluon amplitudes can form a basis for graviton amplitudes up to five points, while also identifying genuine exceptional graviton amplitudes not reducible to gluon products. The authors provide explicit constructions for four- and five-point graviton amplitudes, count independent solutions, and discuss the limits of gauge-gravity relations, including the implications for string theory and color-kinematic duality. The framework paves the way for extending to higher multiplicities, various matter contents, loop orders, and curved backgrounds, with potential applications in effective field theories and beyond-Standard-Model physics.

Abstract

Graviton and gluon scattering are studied from minimal physical assumptions such as Poincare and gauge symmetry as well as unitarity. The assumptions lead to an interesting and surprisingly restrictive set of linear equations. This shows gluon and graviton scattering to be related in many field and string theories, explaining and extending several known results. By systematic analysis exceptional graviton scattering amplitudes are derived which in general dimensions can not be related to gluon amplitudes. The simplicity of the formalism guarantees wide further applicability to gauge and gravity theories.