(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2021., 2021.) Bardavid, Metin.; Değer, Nihat Sadık.
In this thesis we study the theory of Supersymmetric Non-Linear a-Models. We first review the free scalar field theory which can be considered as a Linear a-model. We then discuss the Non-Linear a-model as well as the symmetries of the model with an emphasis on the role of Killing vector fields. After that we turn our attention to study the possible target spaces of these models; these being Kahler and homogeneous manifolds. Finally we introduce the 3-dimensional Non-Linear a-Model with N = 1, 2 and 4 supersymmetries. We show that the D = 3 and N = 2 NLaM has to admit a Kahler target manifold while D = 3 and N = 4 model has to admit a HyperKahler target manifold.