Spinning operators and defects in conformal field theory

Abstract

We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic representation of the Lorentz group. The recipe yields the explicit structures in embedding space, and can be applied to any correlator of local operators, with or without a defect. We then focus on the two-point function of traceless symmetric primaries in the presence of a conformal defect, and explain how to compute the conformal blocks. In particular, we illustrate various techniques to generate the bulk channel blocks either from a radial expansion or by acting with differential operators on simpler seed blocks. For the defect channel, we detail a method to compute the blocks in closed form, in terms of projectors into mixed symmetry representations of the orthogonal group.

arXiv comment44+24 pages

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• Monodromy Defects from Hyperbolic Space
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• On Analytic Bootstrap for Interface and Boundary CFT
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• A dispersion relation for defect CFT
• Conformal Surface Defects in Maxwell Theory are Trivial
• Free energy and defect $C$-theorem in free scalar theory
• New Methods for Conformal Correlation Functions
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• Two Point Functions in Defect CFTs
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• Defect Conformal Blocks from Appell Functions
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• Analytic bootstrap for magnetic impurities
• Universal Spinning Casimir Equations and Their Solutions
• Emitted Radiation and Geometry
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM
• Spacetime Bananas with EOW Branes and Spins