Analytic bootstrap for the localized magnetic field

Abstract

We study the two-point function of local operators in the critical O(N) model in the presence of a magnetic field localized on a line. We use a recently developed conformal dispersion relation to compute the correlator at first order in the $\epsilon$-expansion and we extract the full set of defect and bulk CFT data using the Lorentzian inversion formulae. The only input for the computation of the connected correlator is its discontinuity at first order in perturbation theory, which is determined by the anomalous dimension of a single bulk operator. We discuss possible low-spin ambiguities and perform several diagrammatic checks of our results.

arXiv comment41 pages

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• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• RG Flows and Stability in Defect Field Theories
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• Casimir Forces in CFT with Defects and Boundaries
• Conformal line defects at finite temperature
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations