Correlators of Line Defect and Local Operator in Conformal Field Theories with a Slightly Broken Higher-Spin Symmetry

We study three-dimensional conformal field theories with a large-$N$ limit. Leveraging the framework of slightly broken higher-spin symmetry, we bootstrap correlation functions between the single-trace, local operators and straight, conformal line defects with boundaries. These correlation functions, which depend on a single conformal cross-ratio, encapsulate all bulk-defect operator product expansion coefficients. Concentrating on the quasi-fermionic theory, we explicitly compute all correlators involving the spin-zero and spin-one conserved currents, along with an infinite family of correlators involving the higher-spin currents. Furthermore, we demonstrate that the dependence of these correlators on the defect's shape is fully determined by our bootstrap constraints.