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

## TL;DR

This paper investigates the effects of a monodromy line defect in three-dimensional O(N) models, calculating anomalous dimensions and OPE coefficients using epsilon-expansion and Feynman diagrams, with consistency checks via equations of motion.

## Contribution

It provides the first epsilon-expansion calculations of anomalous dimensions and OPE coefficients for bulk and defect operators in the WF O(N) model with a monodromy line defect.

## Key findings

- Computed anomalous dimensions for bulk and defect operators.
- Derived OPE coefficients involving defect-local fields.
- Validated results through operator equations of motion.

## Abstract

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.