Momentum space conformal three-point functions of conserved currents and a general spinning operator

Abstract

We construct conformal three-point functions in momentum space with a general tensor and conserved currents of spin $1$ and $2$. While conformal correlators in momentum space have been studied especially in the connection with cosmology, correlators involving a tensor of general spin and scaling dimension have not been studied very much yet. Such a direction is unavoidable when we go beyond three-point functions because general tensors always appear as an intermediate state. In this paper, as a first step, we solve the Ward-Takahashi identities for correlators of a general tensor and conserved currents. In particular we provide their expression in terms of the so-called triple-$K$ integrals and a differential operator which relates triple-$K$ integrals with different indices. For several correlators, closed forms without the differential operator are also found.

24+16 pages

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• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• On the consistency of (partially-)massless matter couplings in de Sitter space
• From Schwinger to Wightman: all conformal 3-point functions in momentum space
• $n$-point functions in Conformal Quantum Mechanics: A Momentum Space Odyssey
• Conformal bootstrap in momentum space at finite volume
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Three-point functions of fermionic higher-spin currents in 4D conformal field theory
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point