Path-integral formulation of the Dirichlet string in general backgrounds Original Research Article

We investigate the dynamics of an arbitrary Dirichlet (D-) string in presence of general curved backgrounds following a path-integral formalism. In particular, we consider the interaction of a D-string with the massless excitations of closed string in open bosonic string theory. The background fields induce invariant curvatures on the D-string manifold and the extrinsic curvature can be seen to contain a divergence at the disk boundary. The renormalization of D-string coordinates, next to the leading order in its derivative expansion, is performed to handle the divergence. Then we obtain the generalized Dirac-Born-Infeld action representing the effective dynamics of a D-string in the presence of the non-trivial backgrounds. On the other hand, the D-string acts as a source for the Ramond-Ramond two-form which induces an additional (lower) form due to its coupling to the U(1) gauge invariant fields on the D-string. These forms are reviewed in this formalism for an arbitrary D-string and are encoded in the Wess-Zumino action. Quantization of the D-string collective coordinates, in the U(1) gauge sector, is performed by taking into account the coupling to the lower form and the relevant features of the D-string are analyzed in the presence of background fields.