Path-Integral Formulation of Dirichlet String in General Backgrounds

TL;DR

This paper develops a path-integral approach to analyze the dynamics of Dirichlet strings in curved backgrounds, deriving an effective action and exploring their coupling to background fields and Ramond-Ramond forms.

Contribution

It introduces a generalized Dirac-Born-Infeld action for D-strings in arbitrary backgrounds, including renormalization techniques and coupling to Ramond-Ramond fields.

Findings

Derived the effective D-string action in curved backgrounds.

Analyzed the coupling of D-strings to Ramond-Ramond fields.

Performed quantization of D-string collective coordinates.

Abstract

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 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 re-normalization 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 D-string in presence of the non-trivial backgrounds. On the other hand, 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 is 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 D-string are analyzed in presence of the background fields.