Soft Theorems from Higher Symmetries

TL;DR

This paper establishes new connections between higher symmetries and soft theorems in scattering amplitudes, deriving novel sub-leading and leading soft theorems through algebraic methods without relying on asymptotic symmetries.

Contribution

It introduces a new sub-leading double soft pion theorem for theories with spontaneously-broken 2-group symmetries and provides a novel derivation of the soft photon theorem from Ward identities.

Findings

Derived a sub-leading double soft pion theorem for 2-group symmetries

Provided a new derivation of the soft photon theorem from Ward identities

Used algebraic current methods instead of asymptotic symmetry arguments

Abstract

We describe the connection between spontaneously-broken higher symmetries and soft theorems for scattering amplitudes of their associated Nambu-Goldstone bosons. Our main result is a new sub-leading double soft pion theorem in theories with a spontaneously-broken continuous 2-group global symmetry, which intertwines amplitudes with different numbers of pions and photons. We also provide a novel derivation of the leading soft photon theorem from the Ward identity of an emergent 1-form global symmetry in effective field theories where antiparticles are integrated out. Our derivations of these soft theorems use the algebra of spacetime currents and do not rely on asymptotic symmetries or diagrammatic arguments.