  We consider a possible discretization for the gauge-fixed Green-Schwarz
(two-dimensional) sigma-model action for the Type IIB superstring and use it
for measuring the cusp anomalous dimension of planar $\mathcal{N}=4$ SYM as
derived from string theory. We perform lattice simulations employing a Rational
Hybrid Monte Carlo (RHMC) algorithm and a Wilson-like fermion discretization.
In this preliminary study, we compare our results with the expected behavior
for very large values of $g=\frac{\sqrt{\lambda}}{4\pi}$, which is the
perturbative regime of the sigma-model, and find a qualitative agreement at
finite lattice spacing. For smaller $g$ the continuum limit is obstructed by a
divergence. We also detect a phase in the fermion determinant, whose origin we
explain, which for small $g$ leads to a sign problem not treatable via standard
reweigthing. Results presented here are discussed thoroughly
in~\cite{toappear}.
