The main goal of this work is to investigate the possibility of finding the supersymmetric version of the U(1)-global string model which behaves as a vortex-superfluid. To describe the superfluid phase, we introduce a Lorentz-symmetry breaking background that, in an approach based on supersymmetry, leads to a discussion on the relation between the violation of Lorentz symmetry and explicit soft supersymmetry breakings. We also study the relation between the string configuration and the vortex-superfluid phase. In the framework we settle down in terms of superspace and superfields, we actually establish a duality between the vortex degrees of freedom and the component fields of the Kalb-Ramond superfield. We make also considerations about the fermionic excitations that may appear in connection with the vortex formation.

In this work, we propose the N = 2 and N = 4 supersymmetric extensions of the Lorentz-breaking Abelian Chern-Simons term. We formulate the question of the Lorentz violation in 6 and 10 dimensions to obtain the bosonic sectors of N = 2− and N = 4− supersymmetries, respectively. From this, we carry out an analysis in N = 1 − D = 4 superspace and, in terms of N = 1− superfields, we are able to write down the N = 2 and N = 4 supersymmetric extensions of the Lorentz-violating action term.

We treat the N −extended supergravity in 2 + 1 space-time dimensions as a Yang-Mills gauge field with Chern-Simons action associated to the N -extended Poincaré supergroup. We fix the gauge of this theory within the Batalin-Vilkovisky scheme.

In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N T = 2 SUSY. We start off from the N T = 2, D = 4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables.  2004 Published by Elsevier B.V.