Relativistic Dynamics of Multi-BPS D-vortices and Straight BPS D-strings

TL;DR

This paper analyzes the classical relativistic dynamics of multi-BPS D-vortices and D-strings, revealing their scattering behaviors and reconnection probabilities, with implications for cosmic superstring interactions.

Contribution

It provides an exact classical moduli space dynamics framework for multi-BPS D-vortices and predicts their scattering outcomes, connecting string theory predictions with vortex dynamics.

Findings

Classical motion of D-vortices is governed by a relativistic free-particle Lagrangian.

Head-on collisions result in either 90° or 0°/180° scattering, indicating reconnection or passing through.

Force between non-BPS vortices is repulsive.

Abstract

Moduli space dynamics of multi-D-vortices from D2${\bar {\rm D}}$ (equivalently, parallel straight D-strings from D3${\bar {\rm D}}$3) is systematically studied. For the BPS D-vortices, we show through exact calculations that the classical motion of randomly-distributed $n$ D-vortices is governed by a relativistic Lagrangian of free massive point-particles. When the head-on collision of two identical BPS D-vortices of zero radius is considered, it predicts either 90${}^{\circ}$ scattering or 0${}^{\circ}$ scattering equivalent to 180${}^{\circ}$ scattering. Since the former leads to a reconnection of two identical D-strings and the latter does to a case of their passing through each other, two possibilities are consistent with the prediction of string theory. It is also shown that the force between two non-BPS vortices is repulsive. Although the obtained moduli space dynamics of multi-BPS-D-vortices is exact in classical regime, the quantum effect of an F-string pair production should be included in determining the probabilities of the reconnection and the passing through for fast-moving cosmic superstrings.