Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory

Abstract

We present a systematic method to determine BCJ numerators for one-loop amplitudes that explores the global constraints on the loop momentum dependence. We apply this method to amplitudes in N=4 gauge theory, working out detailed examples up to seven points in both the MHV and the NMHV sectors. The structure of Jacobi identities between BCJ numerators is seen to be closely connected to that of algebraic integrand reductions. We discuss the consequences for one-loop N=8 supergravity amplitudes obtained through the double copy prescription. Moreover, in the MHV sector, we show how to obtain simple BCJ box numerators using a conjectured relationship to amplitudes in self-dual gauge theory. We also introduce simpler trace-type formulas for integrand reductions.

minor corrections, published version

References in corpus (18)

• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Color-kinematic Duality for Form Factors
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Direct Extraction Of One Loop Rational Terms
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• BCJ duality and the double copy in the soft limit
• Relationship Between Gravity and Gauge Scattering in the High Energy Limit
• New Identities among Gauge Theory Amplitudes
• Amplitude for N-Gluon Superstring Scattering
• An algebraic approach to BCJ numerators
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• New Relations for Gauge-Theory Amplitudes with Matter
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• The Complete KLT-Map Between Gravity and Gauge Theories

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• The Kinematic Algebras from the Scattering Equations
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• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
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• Gluons and gravitons at one loop from ambitwistor strings
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• Gauge and Gravity Amplitude Relations
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• Biadjoint wires
• Unraveling conformal gravity amplitudes
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• Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Amplitudes, Hopf algebras and the colour-kinematics duality
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• Dual-color decompositions at one-loop level in Yang-Mills theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Perfecting one-loop BCJ numerators in SYM and supergravity
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• Kinematic Numerators and a Double-Copy Formula for N = 4 Super-Yang-Mills Residues
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
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• Note on symmetric BCJ numerator
• Note on Construction of Dual-trace Factor in Yang-Mills Theory
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• Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
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• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity