Scattering Amplitudes from Soft Theorems and Infrared Behavior

TL;DR

This paper demonstrates that soft theorems and infrared behavior uniquely determine scattering amplitudes across various theories, revealing new corrections and automatic derivations of subleading theorems, thus supporting the idea that asymptotic symmetries fully constrain the S-matrix.

Contribution

It proves that soft theorems uniquely fix scattering amplitudes in many theories and uncovers new corrections and automatic derivations of subleading theorems.

Findings

Soft theorems uniquely determine amplitudes in multiple theories.

Discovered a new higher order correction to the NLSM.

Subleading and subsubleading theorems follow automatically from leading ones.

Abstract

We prove that soft theorems uniquely fix scattering amplitudes in a wide range of theories, including Yang-Mills, gravity, the non-linear sigma model, Dirac-Born-Infeld, dilaton effective theories, extended theories like NLSM$\oplus \phi^3$ or BI$\oplus$YM, as well as some higher derivative corrections to these theories. We conjecture the same is true even when imposing more general soft behavior, simply by assuming the existence of soft operators, or by imposing gauge invariance/the Adler zero only up to a finite order in soft expansions. Besides reproducing known amplitudes, this analysis reveals a new higher order correction to the NLSM, and two interesting facts: the subleading theorem for the dilaton, and the subsubleading theorem for DBI follow automatically from the more leading theorems. These results provide motivation that asymptotic symmetries contain enough information to fully fix a holographic S-matrix.