On the Potentials of Supersymmetric Theories with Gauge-Field Mixing   Terms
  In this letter, we reconsider the delicate issue of symmetry and supersymmetry breakings for gauge theories with gauge-field mixings. The purpose is to study generalyzed potentials in the presence of more than a single gauge potential. In this work, following a stream of investigation on supersymmetric gauge theories without flat directions, we contemplate the possibility of building up D- and F-term potentials by means of a gauge-field mixing in connection with a U(1)x U(1)' -symmetry. We investigate a generalized potential including an N=1 supersymmetric extension of the Maxwell-Chern-Simons model focusing on the study of cosmic string configurations. This analysis sheds some light on the formation of cosmic strings for model with violation of Lorentz symmetry. 
Cristine N. Ferreira, Helder Chavez and Jose A. Helayel-Neto