Geometric Soft Theorems

Abstract

We derive a universal soft theorem for every scattering amplitude with at least one massless particle in an arbitrary theory of scalars. Our results follow from the geometry of field space and are valid for any choice of mass spectrum, potential terms, and higher-derivative interactions. For a vanishing potential, the soft limit of every amplitude is equal to the field-space covariant derivative of an amplitude with one fewer particle. Furthermore, the Adler zero and the dilaton soft theorem are special cases of our results. We also discuss more exotic scenarios in which the soft limit is non-trivial but still universal. Last but not least, we derive new theorems for multiple-soft limits which directly probe the field-space curvature, as well as on-shell recursion relations applicable to two-derivative scalar field theories exhibiting no symmetries whatsoever.

32 pages + refs, 2 figures

References in corpus (9)

• New Relations for Gauge-Theory Amplitudes
• Effective Field Theories from Soft Limits
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• A Periodic Table of Effective Field Theories
• Unitarity Violation and the Geometry of Higgs EFTs
• Double-soft behavior of the dilaton of spontaneously broken conformal invariance
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Cited by in corpus (29)

• Geometry-Kinematics Duality
• Renormalization of the Standard Model Effective Field Theory from Geometry
• Geometry in Scattering Amplitudes
• An EFT hunter's guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes
• Soft Scalars and the Geometry of the Space of Celestial CFTs
• On-Shell Covariance of Quantum Field Theory Amplitudes
• Monolepton production in SMEFT to $\mathcal{O}(1/{\Lambda }^4)$ and beyond
• Symmetries in Celestial CFT${}_d$
• Jet Bundle Geometry of Scalar Field Theories
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
• Inflationary Adler Conditions
• The Geometric $\nu$SMEFT: Operators and Connections
• Anomalous Dimensions via on-shell Methods: Operator Mixing and Leading Mass Effects
• Soft Phonon Theorems
• Walls, bubbles and doom -- the cosmology of HEFT
• $p$-Forms on the Celestial Sphere
• Fractional soft limits
• Renormalising the Field-Space Geometry
• Soft Scalars don't decouple
• Field Space Geometry and Nonlinear Supersymmetry
• Assessing (H)EFT theory errors by pitting EoM against Field Redefinitions
• Real-time observables in de Sitter thermodynamics
• An EFT for anisotropic anti-ferromagnets: gapped Goldstones, pseudo-Goldstones, and phase transitions
• Soft-Theorems for Scalar Particles: The Dilatons Story
• Scalar subleading soft theorems from an infinite tower of charges
• New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Geometric duality between effective field theories I: scattering amplitudes
• Geodesic deviation to all orders via a tangent bundle formalism