Interaction of D-string with F-string: A path-integral formalism

A path integral formalism is developed to study the interaction of an arbit rary curved Dirichlet (D-) string with elementary excitations of the fundum ental (F-) string in bosonic string theory. Up to the next-to-leading order in the derivative expansion, we construct the properly renormalized vertex operator, which generalizes the one previously obtained for a D-particle m oving along a curved trajectory. Using this vertex, an attempt is further m ade to quantize the D-string coordinates and to compute the quantum amplitu de for scattering between elementary excitations of the D- and F-strings. B y studying the dependence on the Liouville mode for the D-string, it is fou nd that the vertex in our approximation consists of an infinite tower of lo cal vertex operators which are conformally invariant on their respective ma ss-shell. This analysis indicates that, unlike the D-particle case, an off- shell extension of the interaction vertex would be necessary to compute the full amplitude and that the realization of symmetry can be quite nontrivia l when the dual extended objects are simultaneously present. Possible futur e directions are suggested.