On-shell functions on the Coulomb branch of $$\mathcal{N}$$ = 4 SYM

Abstract

We study on-shell functions in the kinematic space for the Coulomb branch of $$\mathcal{N}$$ = 4 SYM. We construct BCFW bridges that help us build bigger on-shell functions. As a consequence, we provide on-shell diagram formulations for BCFW shifts that correspond to various mass configurations. We will use this to calculate the quadruple cut for the one-loop amplitude on the Coulomb branch and maximal cuts for higher-loops. We make preliminary comments on finding the inequivalent set of on-shell functions for the Coulomb branch.