Multi-Strings on AdS_3 x S^3 from Matrix String Theory

We analyze the Coulomb branch of Matrix string theory in the presence of NS5-branes. If we regard the components of U(1) gauge fields as the dualized longitudinal coordinates, we obtain the symmetric product of AdS_3 x S^3 x R^4 as the geometry of Coulomb branch. We observe that the absence or presence of the nonzero electric flux determines whether the string propagates in bulk as an ordinary closed string or is forced to live near the boundary. We further discuss the issues of the physical spectrum from the viewpoint of Matrix string theory. We show that the twisted sectors of CFT on the symmetric orbifold, which correspond to glued strings, turn out to yield many chiral primaries that were hitherto considered to be missing. We also comment on the threshold energy in Liouville sector where continuous spectrum begins.Comment: 19pages, no figures, LaTeX; minor correction