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

摘要

We demonstrate the existence of stationary states composed of vortex linesattached to planar dark solitons in scalar Bose-Einstein condensates.Dynamically stable states of this type are found at low values of the chemicalpotential in channeled condensates, where the long-wavelength instability ofdark solitons is prevented. In oblate, harmonic traps, U-shaped vortex linesattached by both ends to a single planar soliton are shown to be long-livedstates. 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 andthereby mimic open strings attached to D-branes in string theory. We show thatthese similarities can be formally established by mapping the Gross-Pitaevskiitheory into a dual effective string theory for open strings via a boson-vortexduality in 3+1 dimensions. Combining a one-form gauge field living on thesoliton plane which couples to the endpoints of vortex lines and a two-formgauge field which couples to vortex lines, we obtain a gauge-invariant dualaction of open vortex lines with their endpoints attached to dark solitons.