Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect

Implications of inserting a conformal, monodromy line defect in three dimensional O($N$) models are studied. We consider then the WF O($N$) model, and study the two-point Green's function for bulk-local fields found from both the bulk-defect expansion and Feynman diagrams. This yields the anomalous dimensions for bulk- and defect-local primaries as well as one of the OPE coefficients as $\epsilon$-expansions to the first loop order. As a check on our results, we study the $(\phi^k)^2{\phi}^j$ operator both using the bulk-defect expansion as well as the equations of motion.