Gravity Amplitudes as Generalized Double Copies

Abstract

Whenever the integrand of a gauge-theory loop amplitude can be arranged into a form where the BCJ duality between color and kinematics is manifest, a corresponding gravity integrand can be obtained simply via the double-copy procedure. However, finding such gauge-theory representations can be challenging, especially at high loop orders. Here we show that we can instead start from generic gauge-theory integrands, where the duality is not manifest, and apply a modified double-copy procedure to obtain gravity integrands that include contact terms generated by violations of dual Jacobi identities. We illustrate this with three-, four- and five-loop examples in N=8 supergravity.

arXiv comment6 pages, 3 figures. Ancillary file included. v2: minor corrections

References in corpus (54)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Gravity as the Square of Gauge Theory
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Black holes and the double copy
• Three-Loop Superfiniteness of N=8 Supergravity
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• The classical double copy for Taub-NUT spacetime
• Explicit BCJ Numerators from Pure Spinors
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• On-shell Techniques and Universal Results in Quantum Gravity
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• The double copy: Bremsstrahlung and accelerating black holes
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Color-Kinematics Duality for QCD Amplitudes
• Yang-Mills origin of gravitational symmetries
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Extensions of Theories from Soft Limits
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
• Dual Identities inside the Gluon and the Graviton Scattering Amplitudes
• Amplitude Relations in Non-linear Sigma Model
• String-inspired BCJ numerators for one-loop MHV amplitudes
• 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
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• A magic pyramid of supergravities
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Twofold Symmetries of the Pure Gravity Action
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• A magic square from Yang-Mills squared
• Gravity On-shell Diagrams
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Colour-Kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms
• On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity
• Graviton and gluon scattering from first principles
• Explicit BCJ numerators of nonlinear sigma model
• BCJ relations from a new symmetry of gauge-theory amplitudes
• Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities

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