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

TL;DR

This paper employs the numerical bootstrap to analyze conformal line defects with $O(2)$ symmetry, exploring defect correlation functions and combining bootstrap with $ ext{epsilon}$-expansion to study specific defect types.

Contribution

It provides a systematic bootstrap analysis of $O(2)$ line defects, including new insights into monodromy and magnetic field line defects, and integrates numerical bootstrap with $ ext{epsilon}$-expansion methods.

Findings

Numerical bounds include known analytic solutions.

Consistent results for monodromy line defect.

Observed intriguing cusps in magnetic field line defect plots.

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 $\varepsilon$-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.