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Can scalars have asymptotic symmetries?

Miguel Campiglia, Leonardo Coito, Sebastian Mizera

TL;DR

The paper probes whether soft theorems for massless scalars can be understood as Ward identities for new asymptotic symmetries. Focusing on Yukawa-type theories with a massless scalar coupled to massive fields, it derives an infinite family of conserved charges and expresses them in terms of asymptotic field data at null, time-like, and spatial infinity. It shows that these charges split into soft and hard components, preserves conservation through matching conditions across infinity, and constructs a spacetime current whose divergence reproduces the charges, signaling a potential symmetry interpretation. However, a fully satisfactory symmetry interpretation remains elusive; the authors discuss obstacles, notably the lack of a clear local symmetry and the need for boundary terms, and suggest connections to dilaton-like scale symmetries as a possible avenue for future work.

Abstract

Recently it has been understood that certain soft factorization theorems for scattering amplitudes can be written as Ward identities of new asymptotic symmetries. This relationship has been established for soft particles with spins $s > 0$, most notably for soft gravitons and photons. Here we study the remaining case of soft scalars. We show that a class of Yukawa-type theories, where a massless scalar couples to massive particles, have an infinite number of conserved charges. This raises the question as to whether one can associate asymptotic symmetries to scalars.

Can scalars have asymptotic symmetries?

TL;DR

The paper probes whether soft theorems for massless scalars can be understood as Ward identities for new asymptotic symmetries. Focusing on Yukawa-type theories with a massless scalar coupled to massive fields, it derives an infinite family of conserved charges and expresses them in terms of asymptotic field data at null, time-like, and spatial infinity. It shows that these charges split into soft and hard components, preserves conservation through matching conditions across infinity, and constructs a spacetime current whose divergence reproduces the charges, signaling a potential symmetry interpretation. However, a fully satisfactory symmetry interpretation remains elusive; the authors discuss obstacles, notably the lack of a clear local symmetry and the need for boundary terms, and suggest connections to dilaton-like scale symmetries as a possible avenue for future work.

Abstract

Recently it has been understood that certain soft factorization theorems for scattering amplitudes can be written as Ward identities of new asymptotic symmetries. This relationship has been established for soft particles with spins , most notably for soft gravitons and photons. Here we study the remaining case of soft scalars. We show that a class of Yukawa-type theories, where a massless scalar couples to massive particles, have an infinite number of conserved charges. This raises the question as to whether one can associate asymptotic symmetries to scalars.

Paper Structure

This paper contains 25 sections, 157 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Spin zero soft theorem as a Ward identity
  3. Conserved charges
  4. Charges in terms of asymptotic fields
  5. Charge conservation
  6. Field equations at time-infinity
  7. Field equations at spatial infinity
  8. Smeared charges
  9. Symmetry interpretation of charges?
  10. Action of charges on asymptotic fields
  11. Spacetime current
  12. Discussion
  13. Soft scalar theorems
  14. Green's functions on $\mathcal{H}^{+}$, $\mathcal{H}^{o}$
  15. (Future) Time-like infinity $\mathcal{H}^+$
  16. ...and 10 more sections

Figures (1)

  • Figure A.1: Two topologies contributing in the soft limit. Wavy line denotes the soft particle, while straight lines denote the hard ones. All momenta are incoming. Only the left topology contributes to the leading soft behavior.