Universal sectors in superconformal defects

Abstract

We study universal features of defect correlation functions in supersymmetric defect CFTs, focusing on four-point functions of the displacement supermultiplet. By perturbing the leading-order correlators at strong coupling, we derive constraints that identify the operators exchanged at next-to-leading order. From this, we determine the conditions under which four-point functions of defect insertions across different theories are equivalent, thereby establishing universality. We confirm these features in examples including the $1/2$ BPS line in $\mathcal{N}=4$ SYM, $\mathcal{N}=2$ gauge theories and ABJM, up to the first subleading order in the strong-coupling expansion. We further analyze the $1/2$ BPS line in 3d $\mathcal{N}=2$ Chern-Simons-matter theories, identifying the preserved defect algebra and the superdisplacement multiplet. Exploiting universality, we find the superdisplacement four-point functions of defect operators and extract the conformal data at first subleading order. Finally, we comment on the $1/3$ BPS Wilson line in ABJM, presenting initial results from the strong-coupling analysis.