Defects, renormalization and conformal field theory

Sammanfattning: Defects in quantum field theories appear in many different contexts and are of great physical interest. Among other things, defects are used to describe the Kondō effect in condensed matter, confinement in quantum chromodynamics, Rényi entropy in quantum information and cosmic strings in string theory. This thesis is a study on the theoretical framework of defects in quantum field theories, and new analytical methods are developed.We study renormalization in the prescence of a defect, and how the conformal symmetry at the fixed points of the corresponding renormalization group flow can be used to bootstrap the bulk two-point correlator. We also study the Coleman-Weinberg mechanism, which allows us to flow along the renormalization group to a first-ordered phase transition.Included in this thesis are several new results. We explain how two-point correlators of mixed bulk-local operators near a boundary can be analytically bootstrapped by exploiting the analytical structure of the conformal blocks. This yields the operator product expansion coefficients in either bootstrap channel. We also consider a sextic bulk-interaction and quartic boundary-interaction near three dimensions, and find the bulk two-point correlator upto two-loops by solving the equation of motion. We then apply the Coleman-Weinberg mechanism to this theory, leading to a spontaneous symmetry breaking of the original O(N)-symmetry. By studying the monodromy of a replica twist defect we learn how a global O(N)-symmetry is broken. We find the anomalous dimensions of the defect-local fields by applying the equation of motion to the bulk-defect operator product expansion. Lastly we study fusion of two scalar Wilson defects. We propose that fusion holds at a quantum level by showing that bare one-point functions stay invariant.