Spin gauge theory, duality and fermion pairing

TL;DR

This paper explores a duality transformation in a 3+1D Abelian Higgs model with electrons, revealing how flux string condensation and a massless antisymmetric tensor field lead to a linearly rising attractive force between electrons, akin to fermion pairing.

Contribution

It introduces a novel duality approach to the Abelian Higgs model, connecting flux string condensation with fermion pairing via an antisymmetric tensor field.

Findings

Flux strings can form in the broken phase of the model.

A massless antisymmetric tensor field mediates a linearly rising attractive force.

Flux string condensation leads to a string Higgs mechanism.

Abstract

We apply duality transformation to the Abelian Higgs model in 3+1 dimensions in the presence of electrons coupled to the gauge field. The Higgs field is in the symmetry broken phase, where flux strings can form. Dualization brings in an antisymmetric tensor potential $B_{\mu\nu}\,$, which couples to the electrons through a nonlocal interaction which can be interpreted as a coupling to the spin current. It also couples to the string worldsheet and gives rise to a string Higgs mechanism via the condensation of flux strings. In the phase where the $B_{\mu\nu}$ field is massless, the nonlocal interaction implies a linearly rising attractive force between the electrons, which can be interpreted as the result of a pair of strings joining the electrons.