BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory

Abstract

We present a field theoretical proof of the conjectured KLT relation which states that the full tree-level scattering amplitude of gluons can be written as a product of color-ordered amplitude of gluons and color-ordered amplitude of scalars with only cubic vertex. To give a proof we establish the KK relation and BCJ relation of color-ordered scalar amplitude using BCFW recursion relation with nonzero boundary contributions. As a byproduct, an off-shell version of fundamental BCJ relation is proved, which plays an important role in our work.

26 pages, 9 figures

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• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
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• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• Amplitude Relations in Non-linear Sigma Model
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• On the kinematic algebra for BCJ numerators beyond the MHV sector
• An algebraic approach to BCJ numerators
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• An Introduction to On-shell Recursion Relations
• UV considerations on scattering amplitudes in a web of theories
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• Off-shell Currents and Color-Kinematics Duality
• Dual-color decompositions at one-loop level in Yang-Mills theory
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
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• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• Unified web for expansions of amplitudes
• Explicit BCJ numerators of nonlinear sigma model
• One-loop SYM-supergravity relation for five-point amplitudes
• Double Copy of Form Factors and Higgs Amplitudes: A mechanism of turning spurious poles in Yang-Mills into physical poles in gravity
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• BCJ, worldsheet quantum algebra and KZ equations
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• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Next-to-MHV Yang-Mills kinematic algebra
• Note on off-shell relations in nonlinear sigma model
• Note on graph-based BCJ relation for Berends-Giele currents
• Boundary Behaviors for General Off-shell Amplitudes in Yang-Mills Theory
• Perturbative Gravity and Gauge Theory Relations -- A Review
• Scattering amplitudes in gauge theories with and without supersymmetry
• The off-shell expansion relation of the Yang-Mills scalar theory
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• A Tale Of Two Amplitudes In High Energy Physics