Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

TL;DR

This paper explores the connections between Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets, revealing equivalences between different physical models through dimensional reduction of a fermion-Chern-Simons framework.

Contribution

It demonstrates the equivalence of a 3D fermion-Chern-Simons model with 2D spinor-Chern-Simons and Heisenberg ferromagnet models via dimensional reduction.

Findings

Dimensional reduction links fermion-Chern-Simons and spinor models.

Identifies static, fixed-chirality sector as equivalent to ferromagnet.

Provides new insights into topological and magnetic phenomena.

Abstract

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.