Vortex lines attached to dark solitons in Bose-Einstein condensates and Boson-Vortex Duality in 3+1 Dimensions

TL;DR

This paper demonstrates the existence and stability of vortex lines attached to dark solitons in Bose-Einstein condensates, and establishes a formal duality between these structures and open strings in string theory.

Contribution

It introduces stable vortex-soliton configurations in BECs and maps the Gross-Pitaevskii theory to a dual string theory framework using boson-vortex duality in 3+1 dimensions.

Findings

Stable vortex-soliton states found at low chemical potentials.

Long-lived U-shaped vortex lines attached to solitons in harmonic traps.

Formal mapping of BEC vortex structures to open strings in string theory.

Abstract

We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the endpoints of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their endpoints attached to dark solitons.