  We study the loop expansion for the low energy effective action for matrix
string theory. For long string configurations we find the result depends on the
ordering of limits. Taking $g_s\to 0$ before $N\to\infty$ we find free strings.
Reversing the order of limits however we find anomalous contributions coming
from the large $N$ limit that invalidate the loop expansion. We then embed the
classical instanton solution into a long string configuration. We find the
instanton has a loop expansion weighted by fractional powers of $N$. Finally we
identify the scaling regime for which interacting long string configurations
have a well defined large $N$ limit. The limit corresponds to large "classical"
strings and can be identified with the "dual of the 't Hooft limit,
$g_{SYM}^2\sim N$.

High Energy Physics - Theory