Remarks on covariant matrix strings

We address the issue of the worldsheet and spacetime covariant formulation for matrix strings. The problem is solved in the limit of vanishing string coupling. To go beyond the g(s) = 0 limit, we propose a topological quantum field theory as a twisted candidate. Our model involves the generalized oc tonionic or SU(4) instanton equations defined in eight dimensions for a sup ersymmetric U(N) Yang-Mills field living on a special holonomy manifold. Th e question of untwisting this matrix model into an anomaly free theory enli ghtens the need for an "extended" 2d-gravity sector, that we suggest could be (partially twisted) W-gravity. (C) 1999 Published by Elsevier Science B. V. All rights reserved.