This thesis contains the study of conformal field theories with flat defects (defect CFT). We consider a generic defect CFT and analyse the symmetry constraints on correlation functions, and then we apply our method to probe the coupling between bulk Maxwell fields and surface defects. To begin with, we provide a practical tool for constructing and investigating correlation functions in defect CFT, directly in physical space. Twopoint correlation functions between any two bulk tensor primaries and between bulk and defect tensor primaries, with arbitrary spin, are considered in detail and then extended to higher-point functions. Consequently, we provide an alternative method, as opposed to the embedding space approach, for studying correlation functions in a generic d-dimensional conformal field theory with a flat p-dimensional defect and d−p = q codimensions. Examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength are tabulated and constraints arising from conservation and equation of motion are analysed. Some explicit examples of defect CFT are also considered: free scalar theory on Rp × (Rq/Z2) and a free four dimensional Maxwell theory on a wedge. Next, we consider the dynamics between a free bulk Maxwell field in four dimensions with matter in a codimension two conformal defect. It is shown that to preserve the conformal symmetry, any such theory which is also reflection positive must be “trivial” and, thus, cannot have interesting interactions. In particular, we show that the defect operator product expansion of the bulk Maxwell field can only contain generalised free fields; the correlation functions of generalised free fields can be evaluated using Wick’s Theorem. As a prelude to surface defects, at the start we briefly consider theories which couples a bulk Maxwell field with matter confined to the surface: either a two-dimensional spinor or two-dimensional scalar. It is shown that such theories end up breaking the conformal symmetry.
Surface Defects in Conformal Field Theory
Shrestha, A. (Author). 1 Mar 2023
Student thesis: Doctoral Thesis › Doctor of Philosophy