Universal sectors in superconformal defects

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 identify constraints on the operators exchanged at next-to-leading order. We then discuss the conditions under which correlation functions of identical superdisplacement components receive contributions only from multiparticle operators built from the same components. This leads to the equivalence between four-point functions of defect insertions across different theories, establishing universality. We confirm these features in examples including the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:math> Bogomol’nyi-Prasad-Sommerfield (BPS) line in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi mathvariant="script">N</c:mi> <c:mo>=</c:mo> <c:mn>4</c:mn> </c:math> super-Yang-Mills, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi mathvariant="script">N</f:mi> <f:mo>=</f:mo> <f:mn>2</f:mn> </f:math> gauge theories and in the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:mi mathvariant="script">N</i:mi> <i:mo>=</i:mo> <i:mn>6</i:mn> </i:mrow> </i:math> Chern–Simons–matter theory of Aharony–Bergman–Jafferis–Maldacena (ABJM), up to the first subleading order in the strong-coupling expansion. We then analyze the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mn>1</l:mn> <l:mo>/</l:mo> <l:mn>2</l:mn> </l:math> BPS Wilson line in 3d <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi mathvariant="script">N</n:mi> <n:mo>=</n:mo> <n:mn>2</n:mn> </n:math> Chern-Simons-matter theories, identifying the preserved defect algebra and the superdisplacement multiplet. Exploiting universality, we find the superdisplacement four-point functions of the defect operators and we extract the conformal data up to the first subleading order. Finally, we comment on the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mn>1</q:mn> <q:mo>/</q:mo> <q:mn>3</q:mn> </q:math> BPS Wilson line in ABJM, providing initial results for the analysis at strong coupling.