Counting Conformal Correlators

Abstract

We introduce simple group-theoretic techniques for classifying conformally-invariant tensor-structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and $n\ge 4$-point functions of general conserved currents, with or without permutation symmetries, and in any spacetime dimension d. (The case n=3 for conserved operators will appear in subsequent work.) Our techniques are useful for bootstrap applications. The rules we derive simultaneously count tensor structures for flat-space scattering amplitudes in d+1 dimensions.

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• Operator bases, $S$-matrices, and their partition functions