Line Defects in Fermionic CFTs

TL;DR

This paper investigates line defects in fermionic conformal field theories within the Gross-Neveu-Yukawa universality class, analyzing their RG flows and fixed points using epsilon expansion and large N techniques, and confirming the g-theorem.

Contribution

It introduces a detailed study of line defects in fermionic CFTs, computing their beta functions and fixed points with novel methods, and verifies the g-theorem for these defects.

Findings

Identified IR stable fixed points for defect couplings.

Computed defect observables at the fixed point.

Confirmed the g-theorem for circular defect RG flow.

Abstract

We study line defects in the fermionic CFTs in the Gross-Neveu-Yukawa universality class in dimensions $2<d<4$. These CFTs may be described as the IR fixed points of the Gross-Neveu-Yukawa (GNY) model in $d=4-\epsilon$, or as the UV fixed points of the Gross-Neveu (GN) model, which can be studied using the large $N$ expansion in $2<d<4$. These models admit natural line defects obtained by integrating over a line either the scalar field in the GNY description, or the fermion bilinear operator in the GN description. We compute the beta function for the defect RG flow using both the epsilon expansion and the large $N$ approach, and find IR stable fixed points for the defect coupling, thus providing evidence for a non-trivial IR DCFT. We also compute some of the DCFT observables at the fixed point, and check that the $g$-function associated with the circular defect is consistent with the $g$-theorem for the defect RG flow.