# Algorithmic construction of SYM multiparticle superfields in the BCJ gauge

## TL;DR

This paper provides explicit formulas and a gauge transformation for constructing super Yang--Mills superfields in the BCJ gauge, facilitating the search for BCJ-satisfying amplitude representations.

## Contribution

It introduces closed formulas and combinatorial maps to systematically obtain superfields in the BCJ gauge, advancing amplitude computation methods.

## Key findings

- Explicit formulas for superfields in BCJ gauge
- Identification of the finite gauge transformation
- Rigorous combinatorial identities proven

## 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.