Spin Impurities, Wilson Lines and Semiclassics

Abstract

We consider line defects with large quantum numbers in conformal field theories. First, we consider spin impurities, both for a free scalar triplet and in the Wilson-Fisher $O(3)$ model. For the free scalar triplet, we find a rich phase diagram that includes a perturbative fixed point, a new nonperturbative fixed point, and runaway regimes. To obtain these results, we develop a new semiclassical approach. For the Wilson-Fisher model, we propose an alternative description, which becomes weakly coupled in the large spin limit. This allows us to chart the phase diagram and obtain numerous rigorous predictions for large spin impurities in $2+1$ dimensional magnets. Finally, we also study $1/2$-BPS Wilson lines in large representations of the gauge group in rank-1 $\mathcal{N}=2$ superconformal field theories. We contrast the results with the qualitative behavior of large spin impurities in magnets.

55 pages + appendices, 13 figures v2 Discussion of effective field theory for Wilson lines shortened, the results remain unchanged; references updated; 53 pages + appendices, 13 figures v3 minor changes, matches published version

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Cited by in corpus (15)

• Anomalies and Symmetry Fractionalization
• Analytic bootstrap for the localized magnetic field
• A dispersion relation for defect CFT
• Phases of Wilson Lines in Conformal Field Theories
• Wilson loop in general representation and RG flow in 1d defect QFT
• Defects in scalar field theories, RG flows and Dimensional Disentangling
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Fixed point annihilation for a spin in a fluctuating field
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Wilson loops in Large Symmetric Representations through a Double-Scaling Limit
• Tunable phase transition in a dissipative two-spin system: A renormalization group study
• Semiclassics of three-dimensional SCFTs from holography
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories