On the Symmetry Foundation of Double Soft Theorems

TL;DR

This paper investigates the foundational symmetry principles behind double soft theorems, revealing two distinct expansion schemes and their implications for deriving soft behaviors from symmetries and unitarity.

Contribution

The work identifies two inequivalent soft limit schemes, clarifies their derivation from symmetries, and explores the connection between soft theorems, locality, and unitarity.

Findings

Type A soft theorems derive from single soft theorems and are non-perturbatively protected.

Type B soft theorems depend on four-point vertices and are not protected.

The analysis extends to general multi-soft theorems and discusses unitarity emergence.

Abstract

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. We show that soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-preturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.