Virtuous Trees at Five and Six Points for Yang-Mills and Gravity

Abstract

We present a particularly nice D-dimensional graph-based representation of the full color-dressed five-point tree-level gluon amplitude. It possesses the following virtues: 1) it satisfies the color-kinematic correspondence, and thus trivially generates the associated five-point graviton amplitude, 2) all external state information is encoded in color-ordered partial amplitudes, and 3) one function determines the kinematic contribution of all graphs in the Yang-Mills amplitude, so the associated gravity amplitude is manifestly permutation symmetric. The third virtue, while shared among all known loop-level correspondence-satisfying representations, is novel for tree-level representations sharing the first two virtues. This new D-dimensional representation makes contact with the recently found multiloop five-point representations, suggesting all-loop, all-multiplicity ramifications through unitarity. Additionally we present a slightly less virtuous representation of the six-point MHV and MHVbar amplitudes which holds only in four dimensions.

11 pages (double-column), 4 figures

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Cited by in corpus (26)

• 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
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Algebras for Amplitudes
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• BCJ duality and the double copy in the soft limit
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Double Copy from Homotopy Algebras
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• Covariant Color-Kinematics Duality
• BCJ duality and double copy in the closed string sector
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Kinematic Lie Algebras From Twistor Spaces
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• Off-shell Currents and Color-Kinematics Duality
• Correlation functions of local composite operators from generalized unitarity
• One-loop SYM-supergravity relation for five-point amplitudes
• Color kinematic symmetric (BCJ) numerators in a light-like gauge
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Note on off-shell relations in nonlinear sigma model
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Scattering Amplitudes in Gauge Theories
• Color-Kinematics Relation from the Feynman Diagram Perspective