Algorithmic construction of SYM multiparticle superfields in the BCJ gauge

Abstract

We write down closed formulas for all necessary steps to obtain multiparticle super Yang--Mills superfields in the so-called BCJ gauge. The superfields in this gauge have obvious applications in the quest for finding BCJ-satisfying representations of amplitudes. As a benefit of having these closed formulas, we identify the explicit finite gauge transformation responsible for attaining the BCJ gauge. To do this, several combinatorial maps on words are introduced and associated identities rigorously proven.

arXiv comment43 pages

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• Classical Double Copy of Worldline Quantum Field Theory
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• Tree-level amplitudes from the pure spinor superstring
• Double Field Theory as the Double Copy of Yang-Mills
• One-loop Correlators and BCJ Numerators from Forward Limits
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• $L_{\infty }$-algebras and the perturbiner expansion
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• The $L_{\infty }$ structure of gauge theories with matter
• A Lie bracket for the momentum kernel
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Color-kinematics duality from the Bern-Kosower formalism
• 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
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Flavour-kinematics duality for Goldstone modes
• Next-to-MHV Yang-Mills kinematic algebra
• The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes
• Note on graph-based BCJ relation for Berends-Giele currents
• Pure spinor formulation of the superstring and its applications