Spinning conformal defects

Abstract

We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with bulk and defect local operators are determined by the conformal symmetry. The operator product expansion (OPE) structure of spinning conformal defects is examined by decomposing it into the spinning defect OPE block that packages all the contribution from a conformal multiplet. The integral representation of the block derived in the shadow formalism is facilitated to deduce recursion relations for correlation functions of two spinning conformal defects. In simple cases, we construct spinning defect correlators by acting differential operators recursively on scalar defect correlators.

arXiv comment36 pages, v2: minor corrections, a reference and notes added, v3: typos corrected

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• Spinning operators and defects in conformal field theory
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• Higher-Point Conformal Blocks in the Comb Channel
• Calogero-Sutherland Approach to Defect Blocks
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Conformal Surface Defects in Maxwell Theory are Trivial
• New Methods for Conformal Correlation Functions
• Two Point Functions in Defect CFTs
• Conformal Bootstrap near the edge
• Correlators of Mixed Symmetry Operators in Defect CFTs
• Efficient Rules for All Conformal Blocks
• Conformal Group Theory of Tensor Structures
• Fusion of conformal defects in four dimensions
• Defect Conformal Blocks from Appell Functions
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Method of images in defect conformal field theories
• Holographic relations for OPE blocks in excited states
• CFTs on curved spaces
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block
• Quantum Information Approaches to Quantum Gravity