Recent results in supersymmetric planar Gauge Theories

Full text follows: In this work we propose to analyse a supersymmetric gauge model in D = 4. It includes a Maxwell field minimally coupled to scalar matter and to another 2-form gauge potential, which in turns couples non-minimally to the scalar. Through a process of dimensional reduction, supplemented by an identification of both gauge fields, we obtain an N = 2-D = 3 supersymmetric gauge theory with a Chern-Simons term and non-minimal coupling to matter. It is shown that the bosonic sector of this model displays topological vortex solutions. The model is still reassessed by means of the Symplectic Projector Method, and we obtain thereby the true dynamical phase space degrees of freedom of the bosonic theory. At last, we reconsider the model by formulating it with the help of superspace techniques. The bosonic component of the central charge present in the supersymmetry algebra is calculated and one shows, as expected, that it is nothing but the topological charge. (author)