Scalar subleading soft theorems from an infinite tower of charges

Abstract

We investigate the emergence of infinite-dimensional symmetries in the absence of gauge invariance by analyzing massless scalar theories. We construct an infinite tower of charges that arise from the subleading equations of motion at null infinity and are built from specific combinations of asymptotic field coefficients. Interestingly, these expressions are finite from the outset, requiring no holographic renormalization. By carefully analyzing the dynamics at spatial infinity, we show that this tower of surface integrals commutes with the S-matrix of the interacting model. As an application, we demonstrate that these symmetries lead to an infinite set of subleading soft relations, valid at leading order in a cubic interaction with massive scalar fields.