Unifying Relations for Scattering Amplitudes

Abstract

We derive new amplitudes relations revealing a hidden unity among wide-ranging theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. Transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.

26 pages+refs, 1 figure for the unified web of theories, v2 matched JHEP version

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Cited by in corpus (89)

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• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Vector Effective Field Theories from Soft Limits
• A new gauge-invariant double copy for heavy-mass effective theory
• Gluons and gravitons at one loop from ambitwistor strings
• Covariant Color-Kinematics Duality
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• Scattering Amplitudes from Soft Theorems and Infrared Behavior
• Pions as Gluons in Higher Dimensions
• The double copy for heavy particles
• The Newman-Penrose Map and the Classical Double Copy
• On the Double Copy for Spinning Matter
• Monopoles, shockwaves and the classical double copy
• Massive Gravity from Double Copy
• UV considerations on scattering amplitudes in a web of theories
• New Soft Theorems for Goldstone Boson Amplitudes
• Lie-algebraic classification of effective theories with enhanced soft limits
• Cosmological Scattering Equations at Tree-level and One-loop
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Radiation of scalar modes and the classical double copy
• Shift symmetries, soft limits, and the double copy beyond leading order
• Note on differential operators, CHY integrands, and unifying relations for amplitudes
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• Kaluza-Klein from Colour-Kinematics Duality for Massive Fields
• Kinematic Hopf algebra for amplitudes and form factors
• Exceptional scalar theories in de Sitter space
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• Expansion of Einstein-Yang-Mills theory by Differential Operators
• Effective Field Theories and Cosmological Scattering Equations
• Transmuting CHY formulae
• Enhanced Soft Limits in de Sitter Space
• Unified web for expansions of amplitudes
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• Soft limits of the wavefunction in exceptional scalar theories
• The Infrared Structure of Exceptional Scalar Theories
• All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity
• Multi-spin soft bootstrap and scalar-vector Galileon
• Analytic Tadpole Coefficients of One-loop Integrals
• Quantum Corrections to Generic Branes: DBI, NLSM, and More
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red
• Inflationary Adler Conditions
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• A Type of Unifying Relation in (A)dS Spacetime
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Matter Couplings and Equivalence Principles for Soft Scalars
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Hidden Conformal Invariance of Scalar Effective Field Theories
• Flavour-kinematics duality for Goldstone modes
• Entanglement and the Double Copy
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• A graphic approach to identities induced from multi-trace Einstein-Yang-Mills amplitudes
• Expansion of tree amplitudes for EM and other theories
• Non-linear Electrodynamics from Massive Gravity
• Berends-Giele currents for extended gravity
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• Double copy for tree-level form factors. Part I. Foundations
• On differential operators and unifying relations for $1$-loop Feynman integrands
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Learning the Simplicity of Scattering Amplitudes
• Next-to-MHV Yang-Mills kinematic algebra
• UV consistency conditions for CHY integrands
• Notes on weight-shifting operators and unifying relations for cosmological correlators
• New relations for tree-level form factors and scattering amplitudes
• Transmuting off-shell CHY integrals in the double-cover framework
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Form factors from string amplitudes
• On the Conformal Symmetry of Exceptional Scalar Theories
• Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Surface Gauge Invariance, Soft Limits and the Transmutation of Gluons into Scalars
• CHY Theory for Several Fields
• On-shell representation and further instances of the 2-split behavior of amplitudes
• Superstring amplitudes meet surfaceology
• Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
• The off-shell expansion relation of the Yang-Mills scalar theory
• A Novel On-Shell Recursive Relation