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Scalar subleading soft theorems from an infinite tower of charges

Matías Briceño1,*, Hernán A. González1,†, and Alfredo Pérez2,3,‡

  • *Contact author: mbricenoc3@correo.uss.cl
  • †Contact author: hernan.gonzalez@uss.cl
  • ‡Contact author: alfredo.perez@uss.cl
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Phys. Rev. D 113, 125033 – Published 29 June, 2026

DOI: https://doi.org/10.1103/5x3x-m2xm

Abstract

We investigate conservation laws in the absence of gauge invariance by analyzing interacting scalar theories with a massless scalar field. 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 at tree level. As an application, we demonstrate that the conservation of these charges leads to an infinite set of subleading soft relations, valid at tree level in a cubic interaction with massive scalar fields.

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Phys. Rev. D 113, 125033– Published 29 June, 2026
  • Received 27 December 2025
  • Accepted 11 June 2026
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