For Yukawa-type couplings φ ψ², between massless scalars φ and other massive particles ψ, an infinite number of soft charges are constructed. These charges generate an asymptotic symmetry which resembles a shift at null infinity, however the corresponding current is not a total derivative (as it is for soft photons or gravitons). Finally, it is suggested that these soft scalars are naturally interpreted as the Nambu-Goldstones of spontaneously broken scale invariance.

In light of recent progress in understanding soft photon, gluon and graviton theorems in terms of asymptotic symmetries, it is natural to ask whether similar reasoning can be applied to scalar field theories. While naively it would be simpler to work in a theory without the complication of spin, in practice it is less obvious how to interpret the asymptotic symmetry when there is no local gauge symmetry (of which e.g. soft photons are the results of large gauge transformations).