The coupling flow of $$ \mathcal{N} $$ = 4 super Yang-Mills theory

We offer a novel perspective on ${\cal N}=4$ supersymmetric Yang-Mills (SYM) theory through the framework of Nicolai map, transformation bosonic fields that allows one to compute quantum correlators in terms free, purely functional measure. Generally, any map is obtained path-ordered exponential so-called coupling flow operator. The latter can be canonically constructed gauge using an N}=1$ off-shell superfield formulation SYM, or alternatively dimensional reduction result from $D=10$ which case we need restrict Landau gauge. propose general operator, arguing it exhibits ambiguity form R-symmetry freedom given by Lie algebra $\mathfrak{su}(4)$. This incorporates our two construction approaches as special points $\mathfrak{su}(4)$ and defines broad class maps for SYM.