We consider the compactification of $M$ theory on a lightlike 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 lightlike 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 $p=0,\dots ,5\mathrm{}$ and clarifies the difficulties for larger values of $p$.

• Received 8 October 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.3577