Spinning Conformal Blocks

Abstract

For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.

29 pages

References in corpus (10)

• Holography from Conformal Field Theory
• Conformal collider physics: Energy and charge correlations
• Writing CFT correlation functions as AdS scattering amplitudes
• Bounds on 4D Conformal and Superconformal Field Theories
• Conformal Partial Waves: Further Mathematical Results
• Bounds in 4D Conformal Field Theories with Global Symmetry
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Central Charge Bounds in 4D Conformal Field Theory
• Recursion Relations for AdS/CFT Correlators
• BCFW for Witten Diagrams

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