Bootstrapping line defects with $O(2)$ global symmetry

Abstract

We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which can either be preserved or partially broken by the presence of the defect. We begin with an agnostic approach and perform a systematic bootstrap study of correlation functions between two canonical operators on the defect: the displacement and the tilt. We then focus on two interesting theories: a monodromy line defect and a localized magnetic field line defect. To this end, we combine the numerical bootstrap with the $\epsilon$-expansion, where we complement existing results in the literature with additional calculations. For the monodromy defect our numerical results are consistent with expectations, with known analytic solutions sitting inside our numerical bounds. For the localized magnetic field line defect our plots show a series of intriguing cusps which we explore.

arXiv comment54 pages, 11 figures

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• Phases of Wilson Lines in Conformal Field Theories
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Line Defect RG Flows in the $\epsilon$ Expansion
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• Defects in scalar field theories, RG flows and Dimensional Disentangling
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Analytic and numerical bootstrap for the long-range Ising model
• Analytic bootstrap for magnetic impurities
• RG Flows and Stability in Defect Field Theories
• The O(N)-flavoured replica twist defect
• Polyakov blocks for the 1D CFT mixed correlator bootstrap
• Casimir Forces in CFT with Defects and Boundaries
• Conformal line defects at finite temperature
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Fine Spectrum from Crude Analytic Bootstrap