A Maxwell-Chern-Simons theory in a Disc Coupled to a Scalar Field on its Boundary

With the advent of the AdS/CFT correspondence and the unraveling of the asymptotic symmetries of relativistic invariant gravitational systems, the last ten to twenty years have seen a great increased interest towards the understanding of quantum field theories in the presence of space-like boundaries. Given this general context, and following up on previous similar studies for Maxwell-like systems, the present Master thesis addresses the dynamics of a field theory in 2+1 spacetime dimensions which combines the usual gauge invariant Maxwell field with a topological Chern-Simons mass term, which is confined to a disk, and is coupled at the disk’s boundary to a massive or massless scalar field. As it turns out, the detailed analysis of this system presented in this work reveals a truly unexpected behavior as soon as the topological Chern-Simons coupling is turned on, however small its value.