Extraordinary Surface Criticalities for Interacting Fermions

Interacting fermions exhibit a rich landscape of surface defects and associated critical phenomena. We investigate novel surface critical behavior in the three-dimensional Gross-Neveu-Yukawa model. For a class of defect renormalization group flows, we obtain exact infrared solutions and show how fermionic anomalies are encoded in the resulting surface dynamics. We further uncover emergent topological and geometric structures in the defect coupling space, and comment on their relation to a defect analogue of the CFT distance conjecture.