Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality

TL;DR

This paper explores non-linear gauge transformations in 10D super Yang--Mills theory, simplifying the structure of multiparticle superfields and elucidating the BCJ duality between color and kinematics.

Contribution

It introduces simplified recursions for multiparticle superfields and relates them to gauge transformations that enforce Lie symmetries, advancing understanding of BCJ duality.

Findings

Streamlined theta-expansion of superfields

Simplified component extraction in pure spinor superspace

Clarified gauge transformations enforcing Lie symmetries

Abstract

Recent progress on scattering amplitudes in super Yang--Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang--Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. In this work we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.