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

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.

LaTeX, 25 pages, 5 figures; several revisions and additions

References in corpus (3)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Vortex-boson duality in four space-time dimensions
• The quantum smectic as a dislocation Higgs phase

Cited by in corpus (6)

• Generalized Symmetries in Condensed Matter
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Theory of the fractional quantum Hall effect in Weyl semimetals
• Topological aspects of brane fields: solitons and higher-form symmetries
• Type-II Bose-Mott insulators
• Global shift symmetry on an ADM hypersurface: Toward emergent gravity