Geometric Soft Theorems

TL;DR

This paper establishes a universal geometric soft theorem for scalar scattering amplitudes, applicable across various theories, revealing deep connections between soft limits, field-space geometry, and symmetries.

Contribution

It introduces a geometric framework for soft theorems in scalar theories, encompassing known results and deriving new multiple-soft theorems linked to field-space curvature.

Findings

Soft theorems derived from field-space geometry.

Universal behavior of amplitudes with massless scalars.

New recursion relations for scalar theories.

Abstract

We derive a universal soft theorem for every scattering amplitude with at least one massless particle in an arbitrary theory of scalars. Our results follow from the geometry of field space and are valid for any choice of mass spectrum, potential terms, and higher-derivative interactions. For a vanishing potential, the soft limit of every amplitude is equal to the field-space covariant derivative of an amplitude with one fewer particle. Furthermore, the Adler zero and the dilaton soft theorem are special cases of our results. We also discuss more exotic scenarios in which the soft limit is non-trivial but still universal. Last but not least, we derive new theorems for multiple-soft limits which directly probe the field-space curvature, as well as on-shell recursion relations applicable to two-derivative scalar field theories exhibiting no symmetries whatsoever.