The space of defects

There are two main concepts that the research question focuses on, defect CFT's (dCFT's) and Conformal Manifolds. CFT is a framework where current research in theoretical physics depends heavily on, especially these days a lot of focus is given in the study of defect CFT's, CFT's where extended objects are introduced in the bulk (defects) and by direct consequence some of the conformal symmetry is broken explicitly. Deforming a CFT by exactly marginal operators produces a Conformal Manifold, a Manifold where each point is a CFT. Doing the same thing in dCFT's deforming with both bulk/defect exactly marginal operators a space of defects is produced. The aim of this project is to address what this space is, what its properties are and in general an in depth understanding of the space of defects. An interesting follow up question is what happens when we introduce supersymmetry, how the Manifold will be enhanced and what new properties will be introduced along with supersymemtry. Most of the tools are evident by now, CFT and dCFT techniques , Geometry and of course extensive use of the current literature.