BCJ duality and double copy in the closed string sector

Abstract

This paper is focused on the loop-level understanding of the Bern-Carrasco-Johansson double copy procedure that relates the integrands of gauge theory and gravity scattering amplitudes. At four points, the first non-trivial example of that construction is one-loop amplitudes in N=2 super-Yang-Mills theory and the symmetric realization of N=4 matter-coupled supergravity. Our approach is to use both field and string theory in parallel to analyze these amplitudes. The closed string provides a natural framework to analyze the BCJ construction, in which the left- and right-moving sectors separately create the color and kinematics at the integrand level. At tree level, in a five-point example, we show that the Mafra-Schlotterer-Stieberger procedure gives a new direct proof of the color-kinematics double copy. We outline the extension of that argument to n points. At loop level, the field-theoretic BCJ construction of N=2 SYM amplitudes introduces new terms, unexpected from the string theory perspective. We discuss to what extent we can relate them to the terms coming from the interactions between left- and right-movers in the string-theoretic gravity construction.

46 pages, 8 figures, 2 tables; v3 significantly revised published version

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Cited by in corpus (36)

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• Color-Kinematics Duality for QCD Amplitudes
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• Closed String Amplitudes as Single-Valued Open String Amplitudes
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• String-inspired BCJ numerators for one-loop MHV amplitudes
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Double Copy from Homotopy Algebras
• Graviton-Photon Scattering
• Double-Copy Constructions and Unitarity Cuts
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Scattering Equations and String Theory Amplitudes
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Superstring loop amplitudes from the field theory limit
• From maximal to minimal supersymmetry in string loop amplitudes
• Gauge $\times$ Gauge on Spheres
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics
• Loop amplitudes monodromy relations and color-kinematics duality
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Explicit BCJ numerators of nonlinear sigma model
• BCJ, worldsheet quantum algebra and KZ equations
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• BCJ Numerators from Differential Operator of Multidimensional Residue
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity