  The consistency of Matrix theory with supergravity requires that in the large
N_c limit terms of order v^4 in the SU(N_c) Matrix effective potential are not
renormalized beyond one loop in perturbation theory. For SU(2) gauge group, the
required non-renormalization theorem was proven recently by Paban, Sethi and
Stern. In this paper we consider the constraints supersymmetry imposes on these
terms for groups SU(N_c) with N_c>2. Non-renormalization theorems are proven
for certain tensor structures, including the structures that appear in the
one-loop effective action. However it is expected other tensor structures can
in general be present, which may suffer renormalization at three loops and
beyond.
