Line Defects with a Cusp in Fermionic CFTs

We study line defects with a cusp in fermionic CFTs arising as fixed points of scalar-fermion theories with Yukawa interactions. These include the Gross-Neveu-Yukawa model and some of its generalizations with additional scalar fields, which can be thought of as UV completions of fermionic theories with quartic interactions. We compute the cusp anomalous dimension in these models to one-loop order in the epsilon expansion near four dimensions, and also to leading order in the large $N$ expansion in $2<d<4$. We discuss several observables that can be extracted from the cusp anomalous dimension, such as the dimensions of the defect changing and defect creation operators, the Casimir energy appearing in the fusion of defects, and the normalization coefficients of the two-point functions of displacement and tilt operators. We provide some estimates of the values of these observables in $d=3$ using the one-loop epsilon expansion and Pad\'e approximants.