Vortices in (abelian) Chern-Simons gauge theory

Understand

The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed.

• Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term.
• Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory with both topological and non-topological self-dual vortices, as found by Hong-Kim-Pac, and by Jackiw-Lee-Weinberg.
• The non-relativistic limit of the latter leads to non-topological Jackiw-Pi vortices with a pure fourth-order potential.