Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Geometrically expanding the BPS vortex of a non-canonical multi-field theory

F. C. E. Lima

TL;DR

The paper addresses how ANO-like magnetic vortices can geometrically expand in a noncanonical multi-field theory with an anomalous magnetic dipole interaction. By employing a noncanonical $O(3)$-sigma model coupled to a gauge field and a real scalar, along with a hyperbolic extension and a BPS decomposition via superpotentials, the authors derive self-dual equations and show that vortices acquire disk-shaped profiles with concentric energy rings while preserving a quantized flux and a fixed BPS energy. The deformation parameter $z$ controls the geometric expansion without changing the total flux or the BPS energy, and numerical Runge–Kutta calculations corroborate the emergence of disk-like vortices and ring-like energy densities. These results connect to Abrikosov vortices in type-II superconductors and hint at applications to flux confinement and sensitive magnetic-field devices, while enriching the theoretical landscape of noncanonical solitons in multi-field theories.

Abstract

Considering a non-canonical multi-field theory, we propose a mechanism of geometric expansion for Abrikosov-Nielsen-Olesen (ANO) vortices. One builds the general setup adopting a non-canonical O(3)-sigma model, non-minimally coupled through an anomalous magnetic dipole interaction to a gauge and real scalar field. By embracing a hyperbolic non-canonical extension, one finds that self-dual vortex configurations undergo geometric expansion, deforming ANO-like vortices into disk-like structures, mitigating their energy, and generating concentric energy rings around the core. Furthermore, these vortices exhibit quantized magnetic flux and degenerate solutions. Finally, we highlight that the analyzed vortices carry energy below the corresponding magnetic flux while preserving a singularity at their origin.

Geometrically expanding the BPS vortex of a non-canonical multi-field theory

TL;DR

The paper addresses how ANO-like magnetic vortices can geometrically expand in a noncanonical multi-field theory with an anomalous magnetic dipole interaction. By employing a noncanonical -sigma model coupled to a gauge field and a real scalar, along with a hyperbolic extension and a BPS decomposition via superpotentials, the authors derive self-dual equations and show that vortices acquire disk-shaped profiles with concentric energy rings while preserving a quantized flux and a fixed BPS energy. The deformation parameter controls the geometric expansion without changing the total flux or the BPS energy, and numerical Runge–Kutta calculations corroborate the emergence of disk-like vortices and ring-like energy densities. These results connect to Abrikosov vortices in type-II superconductors and hint at applications to flux confinement and sensitive magnetic-field devices, while enriching the theoretical landscape of noncanonical solitons in multi-field theories.

Abstract

Considering a non-canonical multi-field theory, we propose a mechanism of geometric expansion for Abrikosov-Nielsen-Olesen (ANO) vortices. One builds the general setup adopting a non-canonical O(3)-sigma model, non-minimally coupled through an anomalous magnetic dipole interaction to a gauge and real scalar field. By embracing a hyperbolic non-canonical extension, one finds that self-dual vortex configurations undergo geometric expansion, deforming ANO-like vortices into disk-like structures, mitigating their energy, and generating concentric energy rings around the core. Furthermore, these vortices exhibit quantized magnetic flux and degenerate solutions. Finally, we highlight that the analyzed vortices carry energy below the corresponding magnetic flux while preserving a singularity at their origin.

Paper Structure

This paper contains 13 sections, 42 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The general framework for vortex structures
  3. The BPS approach
  4. The magnetic vortex configurations
  5. Vortex solution of the multi-field theory
  6. The boundary condition
  7. Physical aspects of magnetic vortices
  8. Topological solution of the scalar field
  9. The sigma field solution
  10. Computational approach
  11. Numerical solutions of the vortices: topological sector of the sigma field
  12. Behavior of the solutions and their phenomenological connection
  13. Summary and conclusions

Figures (4)

  • Figure 1: Scalar field solution $\psi(r)$ vs. $r$ adopting the parameters $\lambda=\nu=1$.
  • Figure 2: Numerical solutions for the field profiles $f(r)$ [figure (a)] and $a(r)$ [figure (b)] vs. $r$ with $N=\lambda=\nu=e=1$.
  • Figure 3: Vortex magnetic field $\vert B(r)\vert$ vs. $r$ with $N=\lambda=\nu=e=1$.
  • Figure 4: BPS energy density $\text{E}_{\text{BPS}}$ vs. $r$ when $N=\lambda=\nu=e=1$.