  The curvature of brane solutions in Yang-Mills matrix models is expressed in
terms of conserved currents associated with global symmetries of the model.
This implies a relation between the Ricci tensor and the energy-momentum tensor
due to the basic matrix model action, without invoking an Einstein-Hilbert
term. The coupling is governed by the extrinsic curvature of the brane
embedding, which arises naturally for compactified brane solutions. The
effective gravity on the brane is thereby related to the compactification
moduli, and protected from quantum corrections due to the relation with global
symmetries.
