  We develop new tools for an in-depth study of our recent proposal for Matrix
Theory. We construct the anomaly-free and finite planar continuum limit of the
ground state with SO(2^{13}) symmetry matching with the tadpole and tachyon
free IR stable high temperature ground state of the open and closed bosonic
string. The correspondence between large N limits and spacetime effective
actions is demonstrated more generally for an arbitrary D25brane ground state
which might include brane-antibrane pairs or NS-branes and which need not have
an action formulation. Closure of the finite N matrix Lorentz algebra
nevertheless requires that such a ground state is simultaneously charged under
all even rank antisymmetric matrix potentials. Additional invariance under the
gauge symmetry mediated by the one-form matrix potential requires a ground
state charged under the full spectrum of antisymmetric (p+1)-form matrix
potentials with p taking any integer value less than 26. Matrix Dbrane
democracy has a beautiful large N remnant in the form of mixed Chern-Simons
couplings in the effective Lagrangian whenever the one-form gauge symmetry is
nonabelian.
