Analytic bootstrap for the localized magnetic field

Understand

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.