Zuhair Khandker

Conformal field theories (CFTs) are highly constrained by symmetry. For instance, based on symmetry considerations alone one can derive constraints on the form of correlators and on the scaling dimensions of certain operators. However, the full implications of symmetry are still far from understood, i.e. we still do not know the extent to which conformal symmetry constrains the space of all possible CFTs. In the non-supersymmetric setting, the embedding-space formalism for CFTs has proven to be an important tool for addressing these questions. After starting with a very general introduction to conformal symmetry, CFTs, and the embedding formalism, I will discuss the generalization of embedding methods to the supersymmetric setting for applications to four-dimensional N=1 superconformal field theories and focus on one such application, constructing manifestly-covariant current correlators.