Double-Copy Constructions and Unitarity Cuts

Abstract

The duality between color and kinematics enables the construction of multiloop gravity integrands directly from corresponding gauge-theory integrands. This has led to new nontrivial insights into the structure of gravity theories, including the discovery of enhanced ultraviolet cancellations. To continue to gain deeper understandings and probe these new properties, it is crucial to further improve techniques for constructing multiloop gravity integrands. In this paper, we show by example how one can alleviate difficulties encountered at the multiloop level by relaxing the color-kinematics duality conditions to hold manifestly only on unitarity cuts instead of globally on loop integrands. As an example, we use a minimal ansatz to construct an integrand for the two-loop four-point nonsupersymmetric pure Yang-Mills amplitude in $D$ dimensions that is compatible with these relaxed color-kinematics duality constraints. We then immediately obtain a corresponding gravity integrand through the double-copy procedure. Comments on ultraviolet divergences are also included.

26 pages, 11 figures, ancillary file, RevTeX

References in corpus (10)

• New Relations for Gauge-Theory Amplitudes
• Black holes and the double copy
• 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
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Yang-Mills origin of gravitational symmetries
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• The Double Copy Structure of Soft Gravitons
• Color kinematic symmetric (BCJ) numerators in a light-like gauge

Cited by in corpus (42)

• The Effective Field Theorist's Approach to Gravitational Dynamics
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Exact solutions for the biadjoint scalar field
• Prescriptive Unitarity
• Topology and Wilson lines: global aspects of the double copy
• Gluons and gravitons at one loop from ambitwistor strings
• Twin Supergravities from Yang-Mills Squared
• Gravitational radiation from the classical spinning double copy
• Weyl doubling
• Monopoles, shockwaves and the classical double copy
• Biadjoint wires
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Kinematic Lie Algebras From Twistor Spaces
• On loop celestial amplitudes for gauge theory and gravity
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• Simplifying $D$-Dimensional Physical-State Sums in Gauge Theory and Gravity
• Full-color three-loop three-point form factors in N=4 SYM
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Non-perturbative Double Copy in Flatland
• Prescriptive Unitarity with Elliptic Leading Singularities
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Beyond the standard model with six-dimensional spinors
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• The Weyl double copy from twistor space
• 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
• On-Shell Perspectives on the Massless Limit of Massive Supergravity