Algorithmic construction of SYM multiparticle superfields in the BCJ gauge

Understand

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.