Renormalization of higher derivative operators in the matrix model

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 supergr avity. It is believed that this is only the case for quantities which are p rotected by non-renormalization theorems. In 0 + 1 and 1 + 1 dimensions, we provide further evidence of a non-renormalization theorem for the upsilon( 4) terms, but also give evidence that there are not such theorems at order upsilon(8) and higher. These results are compatible with known facts about the matrix model. (C) 1998 Published by Elsevier Science B.V. All rights re served.