Soft limits of the wavefunction in exceptional scalar theories

TL;DR

This paper investigates the wavefunctional structure in scalar theories with nonlinearly realized symmetries, deriving soft theorems and bootstrap methods to compute wavefunction coefficients, advancing understanding of these theories' infrared behavior.

Contribution

It introduces a systematic approach to derive wavefunction coefficients in scalar theories with nonlinear symmetries using soft theorems and recursion relations, including new bootstrap techniques.

Findings

Derived soft theorems for scalar theories with nonlinear symmetries

Developed recursion relations for wavefunction coefficients

Established bootstrap methods combining soft theorems and singularity structure

Abstract

We study the structure of the flat space wavefunctional in scalar field theories with nonlinearly realized symmetries. These symmetries imply soft theorems that are satisfied by wavefunction coefficients in the limit where one of the external momenta is scaled to zero. After elucidating the structure of these soft theorems in the nonlinear sigma model, Dirac-Born-Infeld, and galileon scalar theories, we combine them with information about the singularity structure of the wavefunction to bootstrap the wavefunction coefficients of these theories. We further systematize this construction through two types of recursion relations: one that utilizes the flat space scattering amplitude plus minimal information about soft limits, and an alternative that does not require amplitude input, but does require subleading soft information.