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

Understand

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.