  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.
