Perturbative Quantum Gravity as a Double Copy of Gauge Theory

Abstract

In a previous paper we observed that (classical) tree-level gauge theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N = 4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N = 8 supergravity. We also remark on a non-supersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an anti-symmetric tensor and dilaton.

5 pages, 2 figures; v2, minor clarifications and references added

References in corpus (8)

• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Minimal Basis for Gauge Theory Amplitudes
• Three-Loop Superfiniteness of N=8 Supergravity
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Twistor-Strings, Grassmannians and Leading Singularities
• Simplifying the Tree-level Superstring Massless Five-point Amplitude

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• Effective observables for electromagnetic duality from novel amplitude decomposition
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• The ChPT: top-down and bottom-up
• Quantum corrections to tidal Love number for Schwarzschild black holes
• Classical double copy and higher-spin fields
• Double copy of spontaneously broken Abelian gauge theory
• Note on the asymptotic structure of Kerr-Schild form
• A No-go Theorem for a Gauge Vector as a Space-time Goldstone
• New relations for graviton-matter amplitudes
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• One-loop SYM-supergravity relation for five-point amplitudes
• On Absence of 3-loop Divergence in N=4 Supergravity
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• BCJ relations from a new symmetry of gauge-theory amplitudes
• Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme
• One-loop renormalization and the S-matrix
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• Four Loop Scattering in the Nambu-Goto Theory
• ABJM amplitudes and WL at finite N
• Form Factor and Boundary Contribution of Amplitude
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• BRST Symmetry and the Convolutional Double Copy
• Twin conformal field theories
• One-loop diagrams with quadratic propagators from the worldsheet
• On symmetries and dynamics of exotic supermultiplets
• Note on Bonus Relations for N=8 Supergravity Tree Amplitudes
• Gravity loop integrands from the ultraviolet
• On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes
• A scattering amplitudes approach to hard thermal loops
• Unified non-metric (1,0) tensor-Einstein supergravity theories and (4,0) supergravity in six dimensions
• Positivity Bounds on Massive Vectors
• Factorization of cubic vertices involving three different higher spin fields
• Colour-kinematics duality, double copy, and homotopy algebras
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• Generalized Yang-Mills Theory and Gravity
• The Mile High Magic Pyramid
• Minimal models of field theories: SDYM and SDGR
• The Magic Star of Exceptional Periodicity
• Aspects of High Energy Scattering
• Symmetrization of Jordan dialgebras
• Hidden Conformal Invariance of Scalar Effective Field Theories
• Flat-space structure of gluon and graviton in AdS
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Could Planck Star Remnants be Dark Matter?
• Kerr-Schild double copy for Kundt spacetimes of any dimension
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Flavour-kinematics duality for Goldstone modes
• Double Copy of Form Factors and Higgs Amplitudes: A mechanism of turning spurious poles in Yang-Mills into physical poles in gravity
• Non-planar BCFW Grassmannian Geometries
• Bootstrapping Witten diagrams via differential representation in Mellin space
• Perturbative Quantum Field Theory and Homotopy Algebras
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• Asymptotic Weyl double copy in Newman-Penrose formalism
• On Polytopes and Generalizations of the KLT Relations
• Open associahedra and scattering forms
• Non-locality and gravitoelectromagnetic duality
• Entanglement and the Double Copy
• Emergence of Unitarity and Locality from Hidden Zeros at One-Loop Order
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• The double copy: from optics to quantum gravity
• Loop-level double-copy for massive fermions in the fundamental
• On-Shell Structures of MHV Amplitudes Beyond the Planar Limit
• Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
• Poles At Infinity in On-shell Diagrams
• Strong Gravity Approach to QCD and General Relativity
• Fermionic one-loop amplitudes of the RNS superstring
• BCJ, worldsheet quantum algebra and KZ equations
• Massive spin three-half field in a constant electromagnetic background
• Consistent first order action functional for gauge theories
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• Proposed method of combining continuum mechanics with Einstein Field Equations
• Waveforms from Amplitudes
• Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Non-linear Electrodynamics from Massive Gravity
• From lightcone actions to maximally supersymmetric amplitudes
• Proportionality of gravitational and electromagnetic radiation by an electron in an intense plane wave
• On differential operators and unifying relations for $1$-loop Feynman integrands
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Double copy for tree-level form factors. Part I. Foundations
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Group-theoretic relations for partial amplitudes in gauge theories with orthogonal group
• Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups
• New Ambitwistor String Theories
• Symmetries, Spin-2 Scattering Amplitudes, and Equivalence theorems in Warped Five-Dimensional Gravitational Theories
• Learning the Simplicity of Scattering Amplitudes
• KLT Factorization of Winding String Amplitudes
• Infrared behaviour of the one-loop scattering equations and supergravity integrands
• Double copy for tree-level form factors. Part II. Generalizations and special topics
• Nonlocal modification of the Kerr metric
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• Color-Kinematic Numerators for Fermion Compton Amplitudes
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Cosmological Correlators, In-In Formalism and Double Copy
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Background ambiguity and the Gödel double copy
• UV consistency conditions for CHY integrands
• Fixing the non-relativistic expansion of the 1PM potential
• Infrared and Holographic Aspects of the $S$-Matrix in Gauge Theory and Gravity
• Next-to-MHV Yang-Mills kinematic algebra
• A high-precision result for a full-color three-loop three-point form factor in $\mathcal{N}=4$ SYM
• Fermi-Bose cubic couplings in light-cone field theories
• Spinning amplitudes from scalar amplitudes
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Klein and Conformal Superspaces, Split Algebras and Spinor Orbits
• Non-Abelian gauged supergravities as double copies
• Weyl double copy in type D spacetime in four and five dimensions
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• Note on graph-based BCJ relation for Berends-Giele currents
• Field redefinition invariant Lagrange multiplier formalism with gauge symmetries
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Classical gravitational scattering from a gauge-invariant double copy
• New framework for classical double copies
• Permutation in the CHY-Formulation
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• One-loop $N$-point correlators in pure gravity
• The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes
• Five dimensional Weyl double copy
• Non-analytic terms of string amplitudes from partial waves
• Planar Zeros in Gauge Theories and Gravity
• String Theory, Unification and Quantum Gravity
• Taming the 11D pure spinor b-ghost
• The Weyl double copy from twistor space
• Scrambling and Entangling Spinning Particles
• New relations for tree-level form factors and scattering amplitudes
• The symplectic origin of conformal and Minkowski superspaces
• Three-dimensional $\mathrm{SL}(2,\mathbb{R})$ Yang-Mills theory is three-dimensional gravity with background sources
• Off-shell Diagrammatics for Quantum Gravity
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Projectivity of Planar Zeros in Field and String Theory Amplitudes
• Aspects of Gravitational Wave/Particle Duality: Bulk Torsion $\leftrightarrow$ Boundary Gravity Correspondence
• Generalised unitarity for dimensionally regulated amplitudes within FDF
• Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes
• Scattering amplitudes in gauge theories with and without supersymmetry
• Asymptotic safety and quantum gravity amplitudes
• From Twistor-Particle Models to Massive Amplitudes
• Soft Theorems and the KLT-Relation
• Perturbative quantum gravity in double field theory
• Massive Covariant Colour-Kinematics in 3D
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• On-Shell Calculation of Mixed Electromagnetic and Gravitational Scattering
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity
• Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Structure of Massive Gauge/Gravity Scattering Amplitudes, Equivalence Theorems, and Extended Double-Copy with Compactified Warped Space
• The off-shell expansion relation of the Yang-Mills scalar theory
• A Tensor Product Space for Studying the Interaction of Bipartite States of Light with Nanostructures
• Field theory for gravity at all scales
• Superstring amplitudes meet surfaceology
• Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
• Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism
• Influence of a Perfectly Conducting Plate on the Uehling Potential of QED
• Deriving interaction vertices in higher derivative theories
• From colored gravity to electromagnetism
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• Double soft graviton factors from the gravitational Wilson line
• $D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
• Scattering Amplitudes in Gauge Theories
• The Radial Action from Probe Amplitudes to All Orders
• Untwisting the double copy: the zeroth copy as an optical seed
• Einstein gravity as a theory with a SL(2,C) connection double copy
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• BRST Ghost-Vertex Operator in Witten's Cubic Open String Field Theory on Multiple $Dp$-branes
• General Relativity from Quantum Field Theory
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Color-factor symmetry and BCJ relations for QCD amplitudes
• Properties of Yang-Mills scattering forms
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• Weyl double copy in Lifshitz spacetimes
• Cotton Double Copy for Gravitational Waves
• Twisted de Rham theory for string double copy in AdS
• Some finite terms from ladder diagrams in three and four loop maximal supergravity
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands
• Geometric duality between effective field theories I: scattering amplitudes
• On-Shell Perspectives on the Massless Limit of Massive Supergravity
• Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group
• Kerr-Schild Double Copy of the Randall-Sundrum Black String
• Equivalence Theorems and Double-Copy Structure in Scattering Amplitudes of Massive Kaluza-Klein States with Matter Interactions
• Relations and representations of QCD amplitudes
• The seeds of EFT double copy
• A dynamically constrained Yang-Mills theory with Lorentz symmetry group as an alternative theory of gravity
• Perspectives of Perihelion Precession in Torsion Modified Gravity
• NS-NS Spacetimes from Amplitudes
• Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy
• Ambitwistor strings and amplitudes in curved backgrounds
• Extended DBI and its generalizations from graded soft theorems
• Ambitwistor Yang-Mills Theory Revisited
• Multi-centered $\mathcal{N}=2$ BPS black holes: a double copy description
• A Novel On-Shell Recursive Relation
• Gaussian Planck Relics are Ruled-Out as Dark Matter by LIGO
• Scalar Gravity and the Double Copy in the Framework of General Relativity