Vortices in the Maxwell‐Chern‐Simons theory

Abstract

Our aim is to prove rigorously that the Chern-Simons model of Hong, Kim, and Pac [13] and Jackiw and Weinberg [14] (the CS model) and the Abelian Higgs model of Ginzburg and Landau (the AH model, see [15]) are unified by the Maxwell-Chern-Simons theory introduced by Lee, Lee, and Min in [16] (MCS model). In [16] the authors give a formal argument that shows how to recover both the CS and AH models out of their theory by taking special limits for the values of the physical parameters involved. To make this argument rigorous, we consider the existence and multiplicity of periodic vortex solutions for the MCS model and analyze their asymptotic behavior as the physical parameters approach these limiting values. We show that, indeed, the given vortices approach (in a strong sense) vortices for the CS and AH models, respectively. For this purpose, we are led to analyze a system of two elliptic PDEs with exponential nonlinearities on a flat torus. © 2000 John Wiley & Sons, Inc.