String-inspired BCJ numerators for one-loop MHV amplitudes

Abstract

We find simple expressions for the kinematic numerators of one-loop MHV amplitudes in maximally supersymmetric Yang-Mills theory and supergravity, for any multiplicity. The gauge theory numerators satisfy the Bern-Carrasco-Johansson (BCJ) duality between color and kinematics, so that the gravity numerators are simply the square of the gauge theory ones. The duality holds because the numerators can be written in terms of structure constants of a kinematic algebra, which is familiar from the BCJ organization of self-dual gauge theory and gravity. The close connection that we find between one-loop amplitudes in the self-dual case and in the maximally supersymmetric case is the converse to the dimension-shifting formula. The starting point for arriving at our expressions is the dimensional reduction of ten-dimensional amplitudes obtained in the field-theory limit of open superstrings.

31+12 pages, 7 figures. v2: minor corrections, published version

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Cited by in corpus (63)

• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• One-loop amplitudes on the Riemann sphere
• Type D Spacetimes and the Weyl 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
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• Gravity Amplitudes as Generalized Double Copies
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• S-duality and the Double Copy
• Heterotic and bosonic string amplitudes via field theory
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Double Copy from Homotopy Algebras
• Topology and Wilson lines: global aspects of the double copy
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Gluons and gravitons at one loop from ambitwistor strings
• Higher-loop amplitude monodromy relations in string and gauge theory
• Covariant Color-Kinematics Duality
• Double-Copy Constructions and Unitarity Cuts
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Twin Supergravities from Yang-Mills Squared
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Weyl doubling
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Monopoles, shockwaves and the classical double copy
• Unraveling conformal gravity amplitudes
• Tree-level amplitudes from the pure spinor superstring
• Kinematic Lie Algebras From Twistor Spaces
• String amplitudes from field-theory amplitudes and vice versa
• One-loop Correlators and BCJ Numerators from Forward Limits
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Superstring loop amplitudes from the field theory limit
• Collinear limits beyond the leading order from the scattering equations
• Gauge $\times$ Gauge on Spheres
• One-loop monodromy relations on single cuts
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Loop amplitudes monodromy relations and color-kinematics duality
• On integrands and loop momentum in string and field theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Local BCJ numerators for ten-dimensional SYM at one loop
• An $n$-point QCD two-loop amplitude
• One-loop diagrams with quadratic propagators from the worldsheet
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• One-loop superstring six-point amplitudes and anomalies in pure spinor superspace
• BCJ, worldsheet quantum algebra and KZ equations
• Next-to-MHV Yang-Mills kinematic algebra
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• The Weyl double copy from twistor space
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity