Berends-Giele recursions and the BCJ duality in superspace and components

TL;DR

This paper revisits Berends-Giele recursion for gluon amplitudes within ten-dimensional super Yang-Mills, proving connections to pure spinor formulas, exploring superspace representations, and deriving BCJ relations and numerators recursively.

Contribution

It demonstrates the reduction of pure spinor formulas to Berends-Giele, explores superspace amplitude representations, and introduces a recursive method for BCJ numerators.

Findings

Pure spinor formula reduces to Berends-Giele for gluons.

New derivation of BCJ relations using BRST cohomology.

Recursive computation of supersymmetric BCJ numerators.

Abstract

The recursive method of Berends and Giele to compute tree-level gluon amplitudes is revisited using the framework of ten-dimensional super Yang-Mills. First we prove that the pure spinor formula to compute SYM tree amplitudes derived in 2010 reduces to the standard Berends-Giele formula from the 80s when restricted to gluon amplitudes and additionally determine the fermionic completion. Second, using BRST cohomology manipulations in superspace, alternative representations of the component amplitudes are explored and the Bern-Carrasco-Johansson relations among partial tree amplitudes are derived in a novel way. Finally, it is shown how the supersymmetric components of manifestly local BCJ-satisfying tree-level numerators can be computed in a recursive fashion.