Momentum space conformal three-point functions of conserved currents and a general spinning operator
Hiroshi Isono (Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand); Toshifumi Noumi (Department of Physics, Kobe University, Kobe, 657-8501, Japan); Toshiaki Takeuchi (Department of Physics, Kobe University, Kobe, 657-8501, Japan)
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.
