  We study a new class of matrix models, the simplest of which is based on an
Sp(2) symmetry and has a compactification which is equivalent to Chern-Simons
theory on the three-torus. By replacing Sp(2) with the super-algebra Osp(1|32),
which has been conjectured to be the full symmetry group of M theory, we arrive
at a supercovariant matrix model which appears to contain within it the
previously proposed M theory matrix models. There is no background spacetime so
that time and dynamics are introduced via compactifications which break the
full covariance of the model. Three compactifications are studied corresponding
to a hamiltonian quantization in D=10+1, a Lorentz invariant quantization in
D=9+1 and a light cone gauge quantization in D=11=9+1+1. In all cases
constraints arise which eliminate certain higher spin fields in terms of lower
spin dynamical fields. In the SO(9,1) invariant compactification we argue that
the one loop effective action reduces to the IKKT covariant matrix model. In
the light cone gauge compactification the theory contains the standard M theory
light cone gauge matrix model, but there appears an additional transverse five
form field.
