dSCFTs

Defect superconformal field theories (dSCFTs) are quantum field theories that are conformal and supersymmetric in the bulk spacetime and contain a defect of lower dimensionality carrying additional degrees of freedom or imposing boundary conditions, such that the combined system preserves a subset of the bulk superconformal symmetry. The defect can be a line, surface, or higher-dimensional defect, and the amount of preserved symmetry varies, often yielding 1/2-BPS or 1/4-BPS configurations.

dSCFTs can be realized by coupling a higher-dimensional SCFT to a lower-dimensional theory living on the defect, by inserting localized operators that modify the theory, or by string/M-theory constructions in which brane configurations give rise to defect degrees of freedom. In holography, dSCFTs arise from brane intersections or probe branes in AdS backgrounds, yielding gravity duals with defect branes.

The presence of a defect constrains correlation functions through defect conformal symmetry, with correlators obeying both bulk and defect operator product expansions. The spectrum includes bulk operators as well as defect-local operators, and defect conformal blocks can be used in bootstrap approaches to constrain data.

Examples include four-dimensional N=4 super Yang–Mills theory with a 1/2-BPS Wilson line, four-dimensional N=2 theories with 2d surface defects, and three-dimensional theories such as ABJM with line or surface defects. dSCFTs provide a framework for studying localized degrees of freedom, entanglement across defects, and relations to dual holographic descriptions.

See also defect conformal field theory, Wilson loops, surface operators, and holography.