M theory as a matrix extension of Chern–Simons theory

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.