Why is the Matrix Model Correct?

Abstract

We consider the compactification of M theory on a light-like circle as a limit of a compactification on a small spatial circle boosted by a large amount. Assuming that the compactification on a small spatial circle is weakly coupled type IIA theory, we derive Susskind's conjecture that M theory compactified on a light-like circle is given by the finite $N$ version of the Matrix model of Banks, Fischler, Shenker and Susskind. This point of view provides a uniform derivation of the Matrix model for M theory compactified on a transverse torus $T^p$ for $p=0,...,5$ and clarifies the difficulties for larger values of $p$.