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

Alexander Söderberg

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 $ε$-expansions to the first loop order. As a check on our results, we study the $(φ^k)^2φ^j$ operator both using the bulk-defect expansion as well as the equations of motion.

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

Abstract

Implications of inserting a conformal, monodromy line defect in three dimensional O() models are studied. We consider then the WF O() 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 -expansions to the first loop order. As a check on our results, we study the operator both using the bulk-defect expansion as well as the equations of motion.

Paper Structure

This paper contains 18 sections, 84 equations.

Table of Contents

  1. Introduction and Review
  2. Monodromy Line Defect in a Three Dimensional O($N$) Model
  3. Monodromy Action Constraint
  4. Proper Rotation
  5. Improper Rotation
  6. Symmetry Constraints
  7. Green's Function
  8. Green's Function from the Bulk-Defect Expansion
  9. Green's Function from Feynman Rules
  10. Tree-Level Diagram
  11. One-Loop Diagram
  12. Rychkov-Tan Analysis
  13. Proper and Improper O($2$) Solutions
  14. Proper Rotation
  15. Improper Rotation
  16. ...and 3 more sections

Theorems & Definitions (1)

  • Example 1