New BCJ representations for one-loop amplitudes in gauge theories and gravity

Abstract

We explain a procedure to manifest the Bern-Carrasco-Johansson duality between color and kinematics in $n$-point one-loop amplitudes of a variety of supersymmetric gauge theories. Explicit amplitude representations are constructed through a systematic reorganization of the integrands in the Cachazo-He-Yuan formalism. Our construction holds for any nonzero number of supersymmetries and does not depend on the number of spacetime dimensions. The cancellations from supersymmetry multiplets in the loop as well as the resulting power counting of loop momenta is manifested along the lines of the corresponding superstring computations. The setup is used to derive the one-loop version of the Kawai-Lewellen-Tye formula for the loop integrands of gravitational amplitudes.

58 + 15 pages

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Cited by in corpus (63)

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• Heterotic and bosonic string amplitudes via field theory
• A new gauge-invariant double copy for heavy-mass effective theory
• Gluons and gravitons at one loop from ambitwistor strings
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Plane wave backgrounds and colour-kinematics duality
• Unraveling conformal gravity amplitudes
• Tree-level amplitudes from the pure spinor superstring
• Double copy structure of parity-violating CFT correlators
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• String amplitudes from field-theory amplitudes and vice versa
• All-order differential equations for one-loop closed-string integrals and modular graph forms
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• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
• Conformal Gravity from Gauge Theory
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Integrands of loop amplitudes within loop-tree duality
• Superstring loop amplitudes from the field theory limit
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• One-loop monodromy relations on single cuts
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Scattering Forms, Worldsheet Forms and Amplitudes from Subspaces
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
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• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• One-Loop Yang-Mills Integrands from Scattering Equations
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• One-loop diagrams with quadratic propagators from the worldsheet
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• BCJ, worldsheet quantum algebra and KZ equations
• Fermionic one-loop amplitudes of the RNS superstring
• BCJ Numerators from Differential Operator of Multidimensional Residue
• Basis decompositions of genus-one string integrals
• Cyclic products of Szegö kernels and spin structure sums I: hyper-elliptic formulation
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• Pfaffian Diagrams for Gluon Tree Amplitudes
• Advanced tools for basis decompositions of genus-one string integrals
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Massive strings from a haunted field theory
• Group constraint relations for five-point amplitudes in gauge theories with SO(N) and Sp(2N) groups
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands