Perturbative Dynamics of Fractional Strings on Multiply Wound D-strings

TL;DR

This work analyzes fractional string excitations on multiply wound D-strings by turning on gauge holonomies (Wilson lines) on D-brane worldvolumes, inducing twisted boundary conditions that generate fractional moding in the spectrum in units of $2\pi/(nL)$. It develops both a low-energy $U(n)$ gauge theory description and a worldsheet non-linear sigma-model formulation with boundary-changing vertex operators, enabling explicit construction of fractional-string vertex operators and simple scattering amplitudes, including Hawking-emission/absorption scenarios. The results generalize to DD strings and DN strings, predicting spectra quantized in $2\pi/(nL)$ for D-strings and $1/(Q_1 Q_5)$ for DN strings, with degeneracies set by holonomy eigenvalues and gcd relations. Collectively, the work provides a concrete D-brane realization of fractional strings, linking holonomy twisting to black-hole entropy considerations and suggesting avenues to incorporate non-perturbative D-brane dynamics in the broader string theory landscape.

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 $2 π/L Q_1 Q_5$. These fractional states appear naturally in the perturbative spectrum of the theory.

Figures (3)

• Figure 1: Schematic illustration of bound state of two singly wound D-strings and a long D-string wound twice.
• Figure 2: Stringy illustration of fractional strings and its T-dual
• Figure 3: String world sheet amplitude for a process where a wound closed string with momentum $q$ and polarization $\varepsilon_{MN}$ is absorbed by one of the zero branes, creating a pair of fractionally wound open string states with winding numbers $p_1$ and $p_2$.