Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ theory in multi-Regge kinematics: Conformal Regge cut contribution

In this second part of our investigation [1] of the analytic structure of the $2\to 5$ scattering amplitude in the planar limit of $\mathcal{N}=4$ super Yang-Mills theory in multi-Regge kinematics we compute, in all kinematic regions, the Regge-cut contributions at leading order. The results are infrared finite and conformally invariant