Perturbative Dynamics of Fractional Strings on Multiply Wound D-strings

TL;DR

This paper investigates the properties of fractional strings on multiply wound D-branes, describing their states via effective theory and world sheet formulation, and analyzing their scattering amplitudes and quantization in brane bound states.

Contribution

It provides a detailed description of fractional string states in both effective and world sheet frameworks, including their scattering amplitudes and quantization in brane bound states, highlighting their natural emergence in perturbative spectra.

Findings

Fractional strings are characterized by twisted boundary conditions due to gauge holonomy.

Scattering amplitudes for Hawking emission/absorption are computed.

Momentum quantization of fractional DN-strings depends on winding numbers of branes.

Abstract

Fractional strings in the spectrum of states of open strings attached to a multiply wound D-brane is explained. We first describe the fractional string states in the low-energy effective theory where the topology of multiple winding is encoded in the gauge holonomy. The holonomy induces twisted boundary conditions responsible for the fractional moding of these states. We also describe fractional strings in world sheet formulation and compute simple scattering amplitudes for Hawking emission/absorption. Generalization to fractional DN-strings in a 1-brane 5-brane bound state is described. When a 1-brane and a 5-brane wraps $Q_1$ and $Q_5$ times respectively around a circle, the momentum of DN-strings is quantized in units of $2 \pi/L Q_1 Q_5$. These fractional states appear naturally in the perturbative spectrum of the theory.