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

Automated summary

Using the axiomatic framework of Rychkov and Tan, this study examines the critical O(N) vector model with a line defect in (4 - epsilon) dimensions. It is found that the critical value of the defect coupling to the bulk field can be uniquely determined without resorting to diagrammatic calculations, assuming the fixed point is described by defect conformal field theory. Various defect localized operators are also studied using the axiomatic method, where the analyticity of correlation functions is crucial in determining the conformal dimensions of defect composite operators. The leading anomalous dimensions obtained by perturbative calculations are reproduced in all cases, including operators with operator mixing.