Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-06-20
Phys.Lett. B439 (1998) 37-45
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, 1 figure, harvmac.tex, notational errors corrected, references added. Trivial error in section 5 corrected with the
Scientific paper
10.1016/S0370-2693(98)01028-4
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, $g_{SYM}^2\sim N$.
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