  We study an anisotropic variant of the two-dimensional Kardar-Parisi-Zhang
equation, that is relevant to describe growth of vicinal surfaces and has
Gaussian, logarithmically rough, stationary states. While the folklore belief
(based on one-loop Renormalization Group) is that the equation has the same
scaling behaviour as the (linear) Edwards-Wilkinson equation, we prove that, on
the contrary, the non-linearity induces the emergence of a logarithmic
super-diffusivity. This phenomenon is similar in flavour to the
super-diffusivity for two-dimensional fluids and driven particle systems.
