Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions

TL;DR

This paper explores the duality between vortex strings and bosonic phases in 3+1 and higher dimensions, providing a clearer formulation and identifying observable topological defects in Bose-Mott insulators.

Contribution

It offers a new, gauge-free perspective on vortex-string duality in higher dimensions and clarifies the behavior of topological defects in Bose-Mott insulators.

Findings

Demonstrates vortex string condensate behavior from superfluid physics

Identifies line defects in Bose-Mott insulators observable in experiments

Provides a generalized duality framework avoiding gauge fields

Abstract

The vortex-boson (or Abelian-Higgs, XY) duality in 2+1 dimensions demonstrates that the quantum disordered superfluid is equivalent to an ordered superconductor and the other way around. Such a duality structure should be ubiquitous but in 3+1 (and higher) dimensions a precise formulation of the duality is lacking. The problem is that the topological defects become extended objects, strings in 3+1D. We argue how the condensate of such vortex strings must behave from the known physics of the disordered superfluid, namely the Bose-Mott insulator. A flaw in earlier proposals is repaired, and a more direct viewpoint, avoiding gauge fields, in terms of the physical supercurrent is laid out, that also easily generalizes to higher-dimensional and more complicated systems. Furthermore topological defects are readily identified; we demonstrate that the Bose-Mott insulator supports line defects, which may be seen in cold atom experiments.