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

TL;DR

This paper develops a bootstrap approach to compute correlation functions involving line defects and local operators in 3D conformal field theories with slightly broken higher-spin symmetry, revealing shape dependence and explicit correlator forms.

Contribution

It introduces a novel bootstrap framework for defect-local operator correlators in theories with approximate higher-spin symmetry, providing explicit results and shape dependence analysis.

Findings

Computed all correlators involving spin-zero and spin-one currents.

Demonstrated shape dependence of correlators is fully constrained by bootstrap.

Provided explicit formulas for bulk-defect operator product expansion coefficients.

Abstract

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.