Interaction of D-string with F-string: A Path-Integral Formalism

TL;DR

This paper develops a path integral formalism to analyze the interaction between curved D-strings and F-strings in bosonic string theory, constructing a renormalized vertex operator and exploring quantum scattering amplitudes.

Contribution

It introduces a generalized vertex operator for D-strings interacting with F-strings, extending previous models and analyzing conformal invariance and off-shell effects.

Findings

Vertex operator includes an infinite tower of conformally invariant operators

Off-shell extension needed for full amplitude calculation

Interaction involves complex symmetry realization

Abstract

A path integral formalism is developed to study the interaction of an arbitrary curved Dirichlet (D-) string with elementary excitations of the fundumental (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 moving along a curved trajectory. Using this vertex, an attempt is further made to quantize the D-string coordinates and to compute the quantum amplitude for scattering between elementary excitations of the D- and F-strings. By studying the dependence on the Liouville mode for the D-string, it is found that the vertex in our approximation consists of an infinite tower of local vertex operators which are conformally invariant on their respective mass-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 non-trivial when the dual extended objects are simultaneously present. Possible future directions are suggested.