Berends-Giele recursion for double-color-ordered amplitudes

Abstract

Tree-level double-color-ordered amplitudes are computed using Berends--Giele recursion relations applied to the bi-adjoint cubic scalar theory. The standard notion of Berends--Giele currents is generalized to double-currents and their recursions are derived from a perturbiner expansion of linearized fields that solve the non-linear field equations. Two applications are given. Firstly, we prove that the entries of the inverse KLT matrix are equal to Berends--Giele double-currents (and are therefore easy to compute). And secondly, a simple formula to generate tree-level BCJ-satisfying numerators for arbitrary multiplicity is proposed by evaluating the field-theory limit of tree-level string amplitudes for various color orderings using double-color-ordered amplitudes.

15 pages, harvmac TeX, v2: published version

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Cited by in corpus (71)

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• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Exact solutions for the biadjoint scalar field
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Extended solutions for the biadjoint scalar field
• Perturbiner Methods for Effective Field Theories and the Double Copy
• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Tree-level amplitudes from the pure spinor superstring
• Inverse of the String Theory KLT Kernel
• Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions
• UV considerations on scattering amplitudes in a web of theories
• Elliptic scattering equations
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Labelled tree graphs, Feynman diagrams and disk integrals
• $L_{\infty }$-algebras and the perturbiner expansion
• Smoothly Splitting Amplitudes and Semi-Locality
• New recursions for tree-level correlators in (Anti) de Sitter space
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics
• One-loop monodromy relations on single cuts
• CHY-Graphs on a Torus
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• A Lie bracket for the momentum kernel
• An Etude on Recursion Relations and Triangulations
• The $L_{\infty }$ structure of gauge theories with matter
• One-loop off-shell amplitudes from classical equations of motion
• Multiparticle solutions to Einstein's equations
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• Color-kinematics duality from the Bern-Kosower formalism
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• Local BCJ numerators for ten-dimensional SYM at one loop
• Explicit BCJ numerators of nonlinear sigma model
• Planar binary trees in scattering amplitudes
• A Soft Theorem for the Tropical Grassmannian
• A Combinatoric Shortcut to Evaluate CHY-forms
• A Type of Unifying Relation in (A)dS Spacetime
• One-loop diagrams with quadratic propagators from the worldsheet
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• A differential operator for integrating one-loop scattering equations
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• Two dialects for KZB equations: generating one-loop open-string integrals
• New Factorization Relations for Yang Mills Amplitudes
• Celestial Berends-Giele current
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• BCJ Numerators from Differential Operator of Multidimensional Residue
• One-loop $N$-point correlators in pure gravity
• Note on graph-based BCJ relation for Berends-Giele currents
• Massive strings from a haunted field theory
• The off-shell expansion relation of the Yang-Mills scalar theory
• Building Momentum Kernel from Shapovalov Form
• On-shell representation and further instances of the 2-split behavior of amplitudes
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
• Quantum Off-Shell Recursion Relation
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands
• A Novel On-Shell Recursive Relation
• Closed form expression for the 5-point Veneziano amplitude in terms of 4-point amplitudes
• The bi-adjoint scalar $\ell$-loop planar integrand recursion and graded inverse variables