Galilean noncommutative gauge theory: symmetries & vortices

TL;DR

This paper demonstrates that noncommutative Chern-Simons gauge theory with matter fields exhibits exotic Galilean symmetry and constructs vortex solutions by reducing to known self-dual equations.

Contribution

It shows the realization of exotic Galilean symmetry in noncommutative gauge theory and constructs vortex solutions via reduction to self-dual equations.

Findings

Galilean symmetry is compatible with noncommutative gauge theory.

Explicit vortex solutions are constructed.

The symmetry realization is consistent with the Seiberg-Witten map.

Abstract

Noncommutative Chern-Simons gauge theory coupled to nonrelativistic scalars or spinors is shown to admit the ``exotic'' two-parameter-centrally extended Galilean symmetry, realized in a unique way consistent with the Seiberg-Witten map. Nontopological spinor vortices and topological external-field vortices are constructed by reducing the problem to previously solved self-dual equations.