Correlators of Mixed Symmetry Operators in Defect CFTs

Abstract

We use the embedding formalism to study correlation functions of a d-dimensional Euclidean CFT in the presence of a $q$ co-dimensional defect. The defect breaks the global conformal group $SO(d+1,1)$ into $SO(d-q+1,1)\times SO(q)$. We calculate all possible invariant structures that can appear in one-point, two-point and three-point correlation functions of bulk and defect operators in mixed symmetry representation. Their generalization to n-point correlation functions are also worked out. Correlation functions in the presence of a defect, in arbitrary representation of $SO(q)$, are also calculated.

arXiv comment39 pages, 3 figures v2: published version. Corrected typos and results from section 4.3 of v1

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• Free energy and defect $C$-theorem in free scalar theory
• Two Point Functions in Defect CFTs
• Defect Conformal Blocks from Appell Functions
• A Sum Rule for Boundary Contributions to the Trace Anomaly
• Method of images in defect conformal field theories