Candidate for a background independent formulation of M theory

A class of background independent membrane field theories is studied, and several properties are discovered which suggest that they may play a role in a background independent form of M theory. The bulk kinematics of these theories are described in terms of the conformal blocks of an algebra $G_q$ on all oriented, finite genus, two-surfaces. The bulk dynamics is described in terms of causal histories in which time evolution is specified by giving amplitudes to certain local changes of the states. Holographic observables are defined which reside in finite dimensional state spaces associated with boundaries in spacetime. We show here that the natural observables in these boundary state spaces are, when $G_q$ is chosen to be $\mathrm{Spin}\left(D\right)\mathrm{}$ or a supersymmetric extension of it, generalizations of matrix model coordinates in D dimensions. In certain cases the bulk dynamics can be chosen so that the matrix model dynamics is recoverd for the boundary observables. The bosonic and supersymmetric cases in $D=3\mathrm{}$ and $D=9\mathrm{}$ are studied, and it is shown that the latter is, in a certain limit, related to the matrix model formulation of M theory. This correspondence gives rise to a conjecture concerning a background independent form of M theory in terms of which excitations of the background independent membrane field theory that correspond to strings and D0-branes are identified.