# Boson-vortex duality in compressible spin-orbit coupled BECs

## TL;DR

This paper develops a duality framework for spin-orbit coupled Bose-Einstein condensates, revealing how vortices behave and interact under these conditions, including forces and confinement effects.

## Contribution

It introduces a (1+2)-dimensional boson-vortex duality for spin-orbit coupled BECs, deriving generalized hydrodynamic equations and vortex forces.

## Key findings

- Derived generalized hydrodynamic equations with separate phase defect degrees of freedom.
- Calculated the Magnus force on vortices in the presence of spin-orbit coupling.
- Linked vortex confinement to instanton fluctuations in the dual theory.

## Abstract

Using a (1+2)-dimensional boson-vortex duality between non-linear electrodynamics and a two-component compressible Bose-Einstein condensate (BEC) with spin-orbit (SO) coupling, we obtain generalised versions of the hydrodynamic continuity and Euler equations where the phase defect and non-defect degrees of freedom enter separately. We obtain the generalised Magnus force on vortices under SO coupling, and associate the linear confinement of vortices due to SO coupling with instanton fluctuations of the dual theory.