Vortex condensation in the Chern-Simons Higgs model: An existence theorem (Q1894832)

The authors discuss the self-dual model of the Chern-Simons Higgs theory on a \((2 + 1)\)-dimensional Minkowski spacetime. This is a special case of the anyon model. They study stationary solutions over a periodic cell with specific gauge-periodic boundary conditions and prove that there exists a critical value \(\kappa_c\) of the Chern-Simons coupling parameter \(\kappa\) so that for models with \(\kappa < \kappa_c\) admit self-dual doubly periodic vortex solutions. In models with \(\kappa > \kappa_c\) the vortex solutions are absent. An alternative variational approach to the problem is also discussed.