String solutions in Chern-Simons-Higgs model coupled to an axion

We study a d=2+1 dimensional Chern-Simons gauge theory coupled to a Higgs scalar and an axion field, finding the form of the potential that allows the existence of selfdual equations and the corresponding Bogomolny bound for the energy of static configurations. We show that the same conditions allow for the N=2 supersymmetric extension of the model, reobtaining the BPS equations from the supersymmetry requirement. Explicit electrically charged vortex-like solutions to these equations are presented.