Ultraviolet divergences in $D=8$ $N=1$ supersymmetric Yang–Mills theory

We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in the $D=8$ $N=1$ supersymmetric Yang–Mills theory in the planar limit for ladder-type diagrams. We obtain recurrence relations that allow obtaining the leading and subleading divergences in all loops purely algebraically starting from the one-loop diagrams (for the leading poles) and the two-loop diagrams (for the subleading poles). We sum the leading and subleading divergences over all loops using differential equations that are generalizations of the renormalization group equations to nonrenormalizable theories. We discuss the properties of the obtained solutions and the dependence of the constructed counterterms on the scheme.