Geometric Soft Theorems
arXiv:2111.03045 · doi:10.1007/JHEP04(2022)011
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.
arXiv comment32 pages + refs, 2 figures
References in corpus (33)
- Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
- New Relations for Gauge-Theory Amplitudes
- New Recursion Relations for Tree Amplitudes of Gluons
- Perturbative Quantum Gravity as a Double Copy of Gauge Theory
- What is the Simplest Quantum Field Theory?
- New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
- Reduced Effective Lagrangians
- Effective Field Theories from Soft Limits
- Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
- On-Shell Recursion Relations for Effective Field Theories
- A Periodic Table of Effective Field Theories
- A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space
- Geometry of the Scalar Sector
- A Hidden Symmetry of the Galileon
- Soft Bootstrap and Supersymmetry
- Tree-level Amplitudes in the Nonlinear Sigma Model
- New Double Soft Emission Theorems
- Vector Effective Field Theories from Soft Limits
- Recursion relations from soft theorems
- New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order
- Adler's Zero and Effective Lagrangians for Nonlinearly Realized Symmetry
- Unitarity Violation and the Geometry of Higgs EFTs
- New Soft Theorems for Goldstone Boson Amplitudes
- Double Soft Theorems and Shift Symmetry in Nonlinear Sigma Models
- Soft Bootstrap and Effective Field Theories
- Double-soft behavior of the dilaton of spontaneously broken conformal invariance
- On single and double soft behaviors in NLSM
- Symmetry and geometry in generalized Higgs effective field theory -- Finiteness of oblique corrections v.s. perturbative unitarity
- Soft theorems from anomalous symmetries
- On the Supersymmetrization of Galileon Theories in Four Dimensions
- Multi-spin soft bootstrap and scalar-vector Galileon
- Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
- Extended DBI and its generalizations from graded soft theorems
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 and beyond
- Symmetries in Celestial CFT
- Jet Bundle Geometry of Scalar Field Theories
- Lorentz Symmetry and IR Structure of The BFSS Matrix Model
- Inflationary Adler Conditions
- The Geometric 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
- -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