N=4 super-Yang-Mills correlators without anticommuting variables

Quantum correlators of pure supersymmetric Yang-Mills theories in D = 3, 4, 6 and 10 dimensions can be reformulated via the nonlinear and nonlocal transformation (Nicolai map) that maps the full functional measure of the interacting theory to that of a free bosonic theory. As a special application we show that for the maximally extended N = 4 theory in four dimensions, and up to order O(g(2)), all known results for scalar correlators can be recovered in this way without any use of anticommuting variables, in terms of a purely bosonic and ghost-free functional measure for the gauge fields. This includes in particular the dilatation operator yielding the anomalous dimensions of composite operators. The formalism is thus competitive with more standard perturbative techniques.