Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II: Perturbative analysis and all-loop resummation

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. Finally, we extend our findings to the mass deformed theories and discover that the duality still holds true.

Spontaneous symmetry breaking on surface defects

“…2 Sometimes, the transverse rotations SO(d − p) may not be preserved by a conformal defect [21][22][23][24]; this will not be important for our analysis. 3 Notice that when the bulk theory is gapped one can integrate out the bulk degrees of freedom.…”

“…This is because the identities (3.1) and (3.2) imply that the defect currents, when they exist, are primary operators of spin J = 1 and scaling dimension ∆ Ĵ = p − 1. 22 However, the representation theory of the p-dimensional conformal group implies that primaries with ∆ − J = p − 2 and J ≥ 1 are conserved, and therefore a defect current cannot contribute nontrivially to eq. (3.1) since ta (y) = ∂ m Ĵm a (y) = 0.…”

“…We thank P. Kravchuk for useful discussions about this 22. Notice that the Ward identity (3.1) implies that ta transforms as a primary of the p-dimensional conformal…”