Interaction energy of Chern-Simons vortices

The purpose of this paper is to present a computation of the interaction energy of Chern-Simons vortices which are infinitely separated. The results will show the behaviour of the interaction energy as a function of the coupling constant, which measures the relative strength of the matter self-coupling and the electromagnetic coupling. In our normalisation convention, the region λ < 12, the range of matter self interaction exceeds that of the electromagnetic coupling. In the region λ > 12 the opposite is true. We find that vortices attract each other for λ < 12 and repel when λ > 12. When λ = 12 there is a lower bound on the energy. It is possible to saturate the bound if the fields satisfy a set of first order partial differential equations. These results are analogous to the results of Jacobs and Rebbi [L. Jacobs and Rebbi, Phys. Rev. B 19 (1979) 4486], who analysed the Abelian Higgs model.