ANOMALIES AND LARGE-N LIMITS IN MATRIX STRING THEORY

We study the loop expansion for the low energy effective action for ma trix string theory. For long string configurations we find the result depends on the ordering of limits. Taking g(s) --> 0 before N --> infi nity we find free strings. Reversing the order of limits however we fi nd anomalous contributions coming from the large N limit that invalida te the loop expansion. We then embed the classical instanton solution corresponding to a high energy string interaction into a long string c onfiguration. We find the instanton has a loop expansion weighted by f ractional positive powers of N. Finally we identify the scaling regime for which interacting long string configurations have a loop expansio n with 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) similar to N. (C) 1998 Elsevier Science B.V. Al l rights reserved.