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

## TL;DR

This paper constructs momentum space conformal three-point functions involving general tensors and conserved currents, providing explicit solutions using triple-K integrals and differential operators, advancing the understanding of tensor correlators in conformal field theory.

## Contribution

It offers the first detailed solutions for conformal three-point functions with general tensors and conserved currents in momentum space, including explicit formulas and differential relations.

## Key findings

- Explicit expressions for three-point functions involving general tensors.
- Use of triple-K integrals and differential operators to relate different correlators.
- Closed-form solutions for several correlators without differential operators.

## 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.