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Josephson vortices and the Atiyah-Manton construction

Muneto Nitta

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.

Josephson vortices and the 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.

Paper Structure

This paper contains 8 sections, 24 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The model
  3. Sine-Gordon Solitons from ${\bf C}P^1$ Instantons inside a Domain Wall
  4. Domain wall solution
  5. Low-energy effective theory on domain wall world-volume
  6. The sine-Gordon soliton inside the domain wall
  7. Extension and related model
  8. Summary and Discussion

Figures (1)

  • Figure 1: A sine-Gordon soliton in the domain wall describing the ${\bf C}P^1$ lump inside the domain wall. (a) Schematic configuration in the entire space. (b) Points in the ${\bf C}P^1$ target space are denoted by three-dimensional arrows. The north and south poles are denoted by the left and right arrows, respectively.