Double Soft Theorems and Shift Symmetry in Nonlinear Sigma Models

TL;DR

This paper demonstrates that double soft theorems in nonlinear sigma models are universally derived from shift symmetry and Adler's zero condition, independent of the specific coset structure, highlighting their infrared universality.

Contribution

It establishes that double soft theorems follow from shift symmetry and Adler's zero, independent of the coset G/H, revealing their universal infrared nature.

Findings

Double soft theorems are derived from shift symmetry.

The theorems are independent of the coset structure G/H.

The double soft limit depends only on a single four-point interaction.

Abstract

We show both the leading and subleading double soft theorems of the nonlinear sigma model follow from a shift symmetry enforcing Adler's zero condition in the presence of an unbroken global symmetry. They do not depend on the underlying coset G/H and are universal infrared behaviors of Nambu-Goldstone bosons. Although nonlinear sigma models contain an infinite number of interaction vertices, the double soft limit is determined entirely by a single four-point interaction, together with the existence of Adler's zeros.