Rotationally invariant partial-difference formulations for $\mathcal{N}=4$ super Yang-Mills

We consider the field theory formulation for a class of four-dimensional super Yang-Mills (SYM) theories in $2+1$ dimensions. We consider a class of compact ones, in which the Yang-Mills field theory is locally invariant under the $N$-point bisection of the compact subset. We find that the partial-difference formulations of this class are able to solve the four-point functions of the four-dimensional field theory, including the $2+1$-point functions. We also show that this class of partial-difference formulations has a non-perturbative solution to the four-point functions.