The epsilon expansion of the O(N) model with line defect from conformal field theory

We employ the axiomatic framework of Rychkov and Tan to investigate critical O$(N)$ vector model with a line defect in $(4-\epsilon)$ dimensions. assume fixed point is described by conformal field theory show that value coupling bulk uniquely without resorting diagrammatic calculations. also study various localized operators method, where analyticity correlation functions plays crucial role determining dimensions composite operators. In all cases, including operator mixing, we reproduce leading anomalous obtained perturbative