Superspace methods for studying supersymmetric field theories on curved backgrounds

It has been shown, in the 70s-90s, that one basic concept employed in the construction of string theory is Supersymmetry. The general motivation for this thesis is the study of main features of supersymmetric field theories formulated in flat and curved backgrounds, such as on anti De Sitter spaces. We will study in particular the application of superspace and superfield methods of supersymmetric field theories on curved backgrounds. In superspace, we will fix the super-background to be an AdS2 and compute all its supergeometrical objects, We then couple a scalar superfield to the AdS2 background and construct an appropriate Lagrangian with a kinetic and mass term as well as a potential interaction term. We then expand the superfield Lagrangian in terms of the component fields and observe an interesting phenomenon, that in contrast to the flat space, in AdS2 a massless scalar field may have either massless fermionic superpartner or a massive one with the mass inversely proportional to the AdS2 radius. This reflects the influence of the curvature of the background . Lastly, we derive the supersymmetric transformations for component fields, under which the Lagrangian is invariant. These transformations for the supergroup Osp (1/2) containing the isometry group So(2.1) of the AdS2 space as a subgroup.