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($N$) 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 $({\varphi }^k{)}^2{\varphi }^j$ operator both using the bulk-defect expansion as well as the equations of motion.

21 pages

References in corpus (20)

• A Mellin space approach to the conformal bootstrap
• Conformal Bootstrap in Mellin Space
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Long-range critical exponents near the short-range crossover
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Crossing Symmetry in Alpha Space
• Mellin space bootstrap for global symmetry
• Notes on Spinning Operators in Fermionic CFT
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Generalized Wilson-Fisher critical points from the conformal OPE
• The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
• Leading CFT constraints on multi-critical models in d>2
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• The $\epsilon$-expansion of the codimension two twist defect from conformal field theory
• On co-dimension two defect operators

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• Monodromy Defects in Free Field Theories
• On Analytic Bootstrap for Interface and Boundary CFT
• A dispersion relation for defect CFT
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
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• Composite operators near the boundary
• Comments on epsilon expansion of the O$(N)$ model with boundary
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• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM