Anomalies and large N limits in matrix string theory

TL;DR

This paper investigates the behavior of matrix string theory in the large N limit, revealing how different orderings of limits affect the effective action, and identifies regimes where a well-defined large N limit exists for long string configurations.

Contribution

It uncovers the dependence of the loop expansion on the order of limits in matrix string theory and characterizes the scaling regime for consistent large N limits.

Findings

Reversing the order of limits introduces anomalous contributions.

Instanton solutions exhibit fractional powers of N in their loop expansion.

A specific scaling regime ensures a well-defined large N limit for interacting strings.

Abstract

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, $g_{SYM}^2\sim N$.