Spinning Conformal Correlators

Abstract

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.

46 pages, 3 figures; V2: references added; V3: tiny misprint corrected in (A.9)

References in corpus (10)

• Holography from Conformal Field Theory
• Conformal collider physics: Energy and charge correlations
• Writing CFT correlation functions as AdS scattering amplitudes
• On graviton non-Gaussianities during inflation
• Bounds on 4D Conformal and Superconformal Field Theories
• Effective Conformal Theory and the Flat-Space Limit of AdS
• Bounds in 4D Conformal Field Theories with Global Symmetry
• BCFW for Witten Diagrams
• More Holography from Conformal Field Theory
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