Topics in boundary quantum field theory : magnetic edge states in graphene and BCFT orbifold

In this thesis, we investigate two examples of quantum field theory with planar boundaries. In the first part, we study the low energy excitations in a semi-infinite graphene sheet with the zigzag boundary condition. The system is described by a massless Dirac field with boundary condition such that half of the spinor components vanish on the boundary. From the residual continuous and discrete symmetries of the system, we argue that the graphene zigzag edge should be ferromagnetic. In the second part, we study symmetric orbifold boundary conformal field theory (BCFT). We show how to construct Cardy consistent boundary states for this symmetric orbifold BCFT. We also compute the boundary entropy and comment on its relevance to the AdS/BCFT correspondence.Science, Faculty ofPhysics and Astronomy, Department ofGraduat