Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge kinematics

We investigate single-valued polylogarithms in two complex variables, which are relevant for the seven-point remainder function in $N=4$ super-Yang–Mills theory in the multi-Regge regime. After constructing these two-dimensional polylogarithms, we determine the leading logarithmic approximation of the seven-point remainder function up to and including five loops.