Four-Fermion Deformations on Line Defects in QED$_4$ with Yukawas

We elucidate the dynamics induced by a Wilson Line of charge $q$ and electron charge $e$ in $QED_4$ coupled to a real scalar via Yukawa interactions. We observe that there is a range of the fixed product $e^2 q$ with $e\rightarrow 0$ and $q\rightarrow \infty$ for which four-fermion operators play a dominant role for the dynamics of the theory. We uncover the fixed-point dynamics of the theory and analyze their critical behavior.