  $M$-theory is believed to be described in various dimensions by large $N$
field theories. It has been further conjectured that at finite $N$, these
theories describe the discrete light cone quantization (DLCQ) of $M$ theory.
Even at low energies, this is not necessarily the same thing as the DLCQ of
supergravity. It is believed that this is only the case for quantities which
are protected by non-renormalization theorems. In 0+1 and 1+1 dimensions, we
provide further evidence of a non-renormalization theorem for the $v^4$ terms,
but also give evidence that there are not such theorems at order $v^8$ and
higher.
