  We report the results of a set of high precision simulations performed in the
3d gauge Ising model. We evaluated the interquark potential and the first few
energy levels and compared them with the predictions obtained with the
effective Nambu-Goto string and with the free bosonic string. The data are
precise enough to unambiguously distinguish between the free string predictions
and those obtained using the N-G effective string. At large distances we find a
remarkable agreement between Monte Carlo data and N-G predictions for the first
excited energy level, while the free string picture is definitely excluded. As
the interquark distance is decreased (and/or the finite temperature becomes
higher) the Monte Carlo results show larger and larger deviations both from the
N-G and from the free string predictions. In order to better understand this
behaviour we re-derived the effective Nambu-Goto theory result for the Polyakov
loop correlator using a covariant quantization. We chose as boundary conditions
those of an open string attached to two D0-branes at spatial distance $R$, in a
target space with compact euclidean time. Obviously our treatment is fully
consistent only in $d=26$. The extension to generic $d$ requires taking into
account the Liouville mode of Polyakov's formulation. The analogy with the
standard light cone calculation suggests that the contribution due to the
Liouville field can be neglected for large $R$. At shorter scales, the
Liouville mode cannot be neglected and its contribution to the interquark
potential might be the source of the discrepancies with respect to the
effective N-G results that we observe in our Monte Carlo simulations.
