  We report a perturbative calculation of the expectation value of the infinite
straight line Maldacena-Wilson loop in $\mathcal{N}=4$ supersymmetric
Yang-Mills theory to order $g^6$. Thus, we extend the previous perturbative
result by one order. The vacuum expectation value is reformulated in terms of a
non-linear and non-local transformation, the Nicolai map, mapping the full
functional measure of the interacting theory to that of a free bosonic theory.
The results are twofold. The perturbative cancellations of the different
contributions to the Maldacena-Wilson loop are by no means trivial and seem to
resemble those of the circular Maldacena-Wilson loop at order $g^4$.
Furthermore, we argue that our approach to computing quantum correlation
functions is competitive with more standard diagrammatic techniques.
