Vortex-boson duality in four space-time dimensions

TL;DR

This paper formulates a continuum vortex-boson duality in (3+1) dimensions, revealing that a phase fluctuating superconductor maps to a bosonic string theory with implications for Wigner crystals in cuprates.

Contribution

It introduces a continuum vortex-boson duality in four-dimensional spacetime and explores its implications for superconductors and Wigner crystal formation.

Findings

Dual theory involves bosonic strings and a Kalb-Ramond gauge field.

String condensation leads to a Higgs mass for the gauge field.

Wigner crystal emerges as a space-time analog of the Abrikosov lattice.

Abstract

A continuum version of the vortex-boson duality in (3+1) dimensions is formulated and its implications studied in the context of a pair Wigner crystal in underdoped cuprate superconductors. The dual theory to a phase fluctuating superconductor (or superfluid) is shown to be a theory of bosonic strings interacting through a Kalb-Ramond rank-2 tensorial gauge field. String condensation produces Higgs mass for the gauge field and the expected Wigner crystal emerges as an interesting space-time analog of the Abrikosov lattice.