Analytic bootstrap for the localized magnetic field

TL;DR

This paper applies conformal bootstrap techniques to analyze the two-point function in the critical O(N) model with a localized magnetic field, deriving defect and bulk data at first order in epsilon-expansion.

Contribution

It introduces a novel application of conformal dispersion relations and Lorentzian inversion formulas to defect CFTs with a localized magnetic field, providing explicit data extraction methods.

Findings

Computed defect and bulk CFT data at first order in epsilon-expansion.

Derived the correlator using conformal dispersion relations and inversion formulas.

Performed diagrammatic checks confirming the results.

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.