  We study the Z(2) lattice gauge theory in three dimensions, and present high
precision estimates for the first few energy levels of the string spectrum.
These results are obtained from new numerical data for the two-point Polyakov
loop correlation function, which is measured in the 3d Ising spin system using
duality. This allows us to perform a stringent comparison with the predictions
of effective string models. We find a remarkable agreement between the
numerical estimates and the Nambu-Goto predictions for the energy gaps at
intermediate and large distances. The precision of our data allows to
distinguish clearly between the predictions of the full Nambu-Goto action and
the simple free string model up to an interquark distance $r \approx
10/\sqrt{\sigma}$. At the same time, our results also confirm the breakdown of
the effective picture at short distances, supporting the hypothesis that terms
which are not taken into account in the usual Nambu-Goto string formulation
yield a non-trivial shift to the energy levels. Furthermore, we discuss the
theoretical implications of these results.
