2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53703The two-dimensional self-dual Chern-Simons equations are equivalent to the conditions for static, zero-energy vortex-like solutions of the (2+1) dimensional gauged nonlinear Schrödinger equation with Chern-Simons matter-gauge coupling. The finite charge vacuum states in the Chern-Simons theory are shown to be gauge equivalent to the finite action solutions to the two-dimensional chiral model (or harmonic map) equations. The Uhlenbeck-Wood classification of such harmonic maps into the unitary groups thereby leads to a complete classification of the vacuum states of the Chern-Simons model. This construction also leads to an interesting new relationship between $SU(N)$ Toda theories and the $SU(N)$ chiral model.10 pages, LaTeX file, with 1 figure PostScript file "vortex.ps" included, and "epsf.sty" appended. UCONN-93-8High Energy Physics - Theorytext