Josephson vortices and the Atiyah-Manton construction

TL;DR

This paper demonstrates how Josephson vortices emerge as sine-Gordon solitons in a U(1) gauge theory with scalar fields, linking them to instantons and providing a physical realization of a lower-dimensional Atiyah-Manton construction.

Contribution

It introduces a novel setup where Josephson vortices are realized as sine-Gordon solitons, connecting gauge theory, solitons, and instantons in a new physical context.

Findings

Sine-Gordon solitons appear in the effective theory of a domain wall.

These solitons are identified as vortices or CP(1) sigma model instantons.

The setup provides a physical realization of a lower-dimensional Atiyah-Manton construction.

Abstract

We show that sine-Gordon solitons appear in the low-energy effective theory of a domain wall in a U(1) gauge theory with two charged complex scalar fields with masses, if we introduce the Josephson interaction term between the scalar fields. We identify these sine-Gordon solitons as vortices or CP(1) sigma model instantons in the bulk, which are absorbed into the domain wall world-volume. These vortices can be called as Josephson vortices since they appear in Josephson junctions of two superconductors. This set up gives a physical realization of a lower dimensional analogue of Atiyah-Manton construction of Skyrmions from instanton holonomy.