Gravity as the Square of Gauge Theory

Abstract

We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By "squaring" the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.

32 pages, 4 figures

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Cited by in corpus (282)

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• Observables and amplitudes for spinning particles and black holes
• Explicit BCJ Numerators from Pure Spinors
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• A Periodic Table of Effective Field Theories
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
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• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• Algebras for Amplitudes
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• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Color-kinematic Duality for Form Factors
• Yang-Mills origin of gravitational symmetries
• Scattering on plane waves and the double copy
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Gravitational Radiation from Color-Kinematics Duality
• Closed String Amplitudes as Single-Valued Open String Amplitudes
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Basics of Generalized Unitarity
• Type D Spacetimes and the Weyl Double Copy
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Spinning particles, axion radiation, and the classical double copy
• The self-dual classical double copy, and the Eguchi-Hanson instanton
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• BCJ duality and the double copy in the soft limit
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Bound states and the classical double copy
• Linking the Singularities of Cosmological Correlators
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• Closed Superstring Amplitudes, Single-Valued Multiple Zeta Values and Deligne Associator
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• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
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• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
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• Chiral Higher Spin Theories and Self-Duality
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• Generic multiloop methods and application to N=4 super-Yang-Mills
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• S-duality and the Double Copy
• Color/Kinematics Duality in AdS${}_4$
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Expansion of Einstein-Yang-Mills Amplitude
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Screw-symmetric gravitational waves: a double copy of the vortex
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Double Copy from Homotopy Algebras
• Graviton-Photon Scattering
• Topology and Wilson lines: global aspects of the double copy
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• Double Copy for Celestial Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
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• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Shifting Spin on the Celestial Sphere
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Gluons and gravitons at one loop from ambitwistor strings
• The Classical Double Copy of a Point Charge
• The convolutional double copy: a case study with a point
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• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• Extended solutions for the biadjoint scalar field
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• An algebraic approach to BCJ numerators
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• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
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• Expansion of All Multitrace Tree Level EYM Amplitudes
• Ehlers as EM duality in the double copy
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• On factorizations in perturbative quantum gravity
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• The double copy for heavy particles
• Weyl doubling
• Classical and quantum double copy of back-reaction
• Sources in the Weyl double copy
• On the Double Copy for Spinning Matter
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• Kerr-Newman from Minimal Coupling
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• Gauge and Gravity Amplitude Relations
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• Biadjoint wires
• Unraveling conformal gravity amplitudes
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• Gravity as a diffeomorphism invariant gauge theory
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• Kinematic Lie Algebras From Twistor Spaces
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• UV considerations on scattering amplitudes in a web of theories
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• The Radiative Double Copy for Einstein-Yang-Mills Theory
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• One-loop Correlators and BCJ Numerators from Forward Limits
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
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• Einstein-Maxwell theory and the Weyl double copy
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• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
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• Alternative formulations of the twistor double copy
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• Twistor Space Origins of the Newman-Penrose Map
• Conformal Gravity from Gauge Theory
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• On the Lagrangian formulation of the double copy to cubic order
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• The double copy of the multipole expansion
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• Virtuous Trees at Five and Six Points for Yang-Mills and Gravity
• Why is the Weyl double copy local in position space?
• Amplitudes at Infinity
• Radiation of scalar modes and the classical double copy
• Gauge $\times$ Gauge on Spheres
• Non-perturbative aspects of the self-dual double copy
• Isometries and the double copy
• Shift symmetries, soft limits, and the double copy beyond leading order
• Graviton and gluon scattering from first principles
• Off-shell Currents and Color-Kinematics Duality
• Comment on the Identities of the Gluon Tree Amplitudes
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Relations of loop partial amplitudes in gauge theory by Unitarity cut method
• The single copy of the gravitational holonomy
• More on the Classical Double Copy in Three Spacetime Dimensions
• Dual-color decompositions at one-loop level in Yang-Mills theory
• Loop amplitudes monodromy relations and color-kinematics duality
• The critical ultraviolet behaviour of N=8 supergravity amplitudes
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Higher-derivative Heterotic Double Field Theory and Classical Double Copy
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Properties of scattering forms and their relation to associahedra
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• On Primary Relations at Tree-level in String Theory and Field Theory
• Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• Exact results for scattering on ultra-short plane wave backgrounds
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• Non-planarity through unitarity in ABJM
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• An Introduction to Webs
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• Chiral Squaring
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Soft-collinear gravity beyond the leading power
• Double copy for Lagrangians at trilinear order
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
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• Near-Extremal Black Branes with n*3 Entropy Growth
• Beyond the standard model with six-dimensional spinors
• Gravitational soft theorem from emergent soft gauge symmetries
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• The gravitational cusp anomalous dimension from AdS space
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Gravitational Dyonic Amplitude at One-Loop and its Inconsistency with the Classical Impulse
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• Gravity and Mirror Gravity in Plebanski Formulation
• Explicit BCJ numerators of nonlinear sigma model
• Quantum corrections to tidal Love number for Schwarzschild black holes
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Regularized Weyl double copy
• One-loop SYM-supergravity relation for five-point amplitudes
• One-loop renormalization and the S-matrix
• Classical double copy and higher-spin fields
• New relations for graviton-matter amplitudes
• ABJM amplitudes and WL at finite N
• Gravitons, Bose-symmetry, and Bonus-scaling
• Challenges of D=6 N=(1,1) SYM Theory
• On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes
• Color kinematic symmetric (BCJ) numerators in a light-like gauge
• On symmetries and dynamics of exotic supermultiplets
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Factorization of cubic vertices involving three different higher spin fields
• Aspects of High Energy Scattering
• Asymptotic freedom from the two loop term of the $\beta$-function in a cubic theory
• Renormalization-Group Behavior of ${\varphi }^3$ Theories in $d=6$ Dimensions
• The n-point MHV one-loop Amplitude in N=4 Supergravity
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Double Copy of Form Factors and Higgs Amplitudes: A mechanism of turning spurious poles in Yang-Mills into physical poles in gravity
• Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
• Entanglement and the Double Copy
• The double copy: from optics to quantum gravity
• Berends-Giele currents for extended gravity
• From lightcone actions to maximally supersymmetric amplitudes
• BCJ, worldsheet quantum algebra and KZ equations
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• On differential operators and unifying relations for $1$-loop Feynman integrands
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Holonomies of gauge fields in twistor space 3: gravity as a square of N=4 theory
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Infrared and Holographic Aspects of the $S$-Matrix in Gauge Theory and Gravity
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• Next-to-MHV Yang-Mills kinematic algebra
• Note on graph-based BCJ relation for Berends-Giele currents
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Note on off-shell relations in nonlinear sigma model
• New framework for classical double copies
• The Weyl double copy from twistor space
• Three-dimensional $\mathrm{SL}(2,\mathbb{R})$ Yang-Mills theory is three-dimensional gravity with background sources
• Off-shell Diagrammatics for Quantum Gravity
• Scattering amplitudes in gauge theories with and without supersymmetry
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity
• A Tensor Product Space for Studying the Interaction of Bipartite States of Light with Nanostructures
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• The Radial Action from Probe Amplitudes to All Orders
• Note on the non-adjacent BCFW deformations
• From colored gravity to electromagnetism
• Intersection of Yang-Mills Theory with Gauge Description of General Relativity
• Color-factor symmetry and BCJ relations for QCD amplitudes
• Scalar Gravity and the Double Copy in the Framework of General Relativity
• Ambitwistor Yang-Mills Theory Revisited
• Categorical generalization of BF theory coupled to gravity
• Ambitwistor strings and amplitudes in curved backgrounds
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Weyl double copy in Lifshitz spacetimes
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• Properties of Yang-Mills scattering forms
• Graviton scattering amplitudes and Pure Connection Formulation of GR