Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation

TL;DR

This paper analyzes mesonic line operators in Chern-Simons-matter theories, classifying their properties through all-loop resummation, identifying stable and unstable conformal lines, and matching operators across bosonic and fermionic models.

Contribution

It provides a comprehensive classification of mesonic line operators in large N Chern-Simons-matter theories, including their conformal properties and operator matching between bosonic and fermionic cases.

Findings

Identifies two conformal line operators: one stable, one unstable.

Explicitly computes boundary operator dimensions and spins at finite coupling.

Establishes operator correspondence between bosonic and fermionic theories.

Abstract

We study mesonic line operators in Chern-Simons theories with bosonic or fermionic matter in the fundamental representation. In this paper, we elaborate on the classification and properties of these operators using all loop resummation of large $N$ perturbation theory. We show that these theories possess two conformal line operators in the fundamental representation. One is a stable renormalization group fixed point, while the other is unstable. They satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two mesonic line operators. The boundary operators on which the lines can end are classified by their conformal dimension and transverse spin, which we compute explicitly at finite 't Hooft coupling. We match the operators in the bosonic and fermionic theories.