Soft theorems and spontaneous symmetry breaking

Abstract

The soft photon and soft graviton theorems of Weinberg are known to derive from conservation laws associated with asymptotic symmetries. Within the corresponding classical theories, one often speaks of spontaneous symmetry breaking and vacuum degeneracy, but a genuine quantum description of this phenomenon has largely been lacking. Here we establish spontaneous breaking of asymptotic symmetries and the existence of Goldstone `particles' using exclusively the language of quantum field theory. This is made possible through the reformulation of massless scattering theory in terms of carrollian conformal field theory, and the observation that soft theorems correspond to Ward identities of broken symmetries. A suitable version of Goldstone theorem shows that there must exist zero-momentum particles described by conformal fields on the celestial sphere, in agreement with the common lore. More specifically, these belong to unitary representations in the discrete series of the Lorentz group, and are therefore naturally equipped with logarithmic two-point functions. We discuss the relevance of these observations to the problem of infrared divergences that scattering amplitudes suffer from.