Why is the Matrix Model Correct?

TL;DR

This paper derives and clarifies the Matrix model description of M theory compactified on a light-like circle, connecting it to weakly coupled type IIA theory and extending to various transverse torus compactifications.

Contribution

It provides a uniform derivation of the Matrix model for M theory on a light-like circle and clarifies challenges for higher-dimensional tori.

Findings

Derivation of the Matrix model from weakly coupled type IIA theory.

Extension of the Matrix model to transverse tori $T^p$ for $p=0,...,5$.

Clarification of difficulties for larger $p$.

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 $p$.