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Double-soft theorems, like its single-soft counterparts, arises from theunderlying symmetry principles that constrain the interactions of masslessparticles. While single soft theorems can be derived in a non-perturbativefashion by employing current algebras, recent attempts of extending such anapproach to known double soft theorems has been met with difficulties. In thiswork, 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 fortype A scheme can simply be derived from single soft theorems, and are thusnon-preturbatively protected. For type B, the information of the four-pointvertex is required to determine the corresponding soft theorems, and thus arein general not protected. This argument can be readily extended to generalmulti-soft theorems. We also ask whether unitarity can be emergent fromlocality together with the two kinds of soft theorems, which has not been fullyinvestigated before.

On the Symmetry Foundation of Double Soft Theorems