Momentum space CFT correlators of non-conserved spinning operators

TL;DR

This paper derives explicit formulas for 3-point correlation functions involving non-conserved spinning operators in momentum space within conformal field theories, addressing divergences and conformal Ward identities.

Contribution

It provides the first general expression for 3-point functions with two non-conserved spins and a conserved current, including explicit cases and divergence analysis.

Findings

Explicit 3-point function formulas for spins 1 and 2

Analysis of divergences when conformal dimensions coincide

Derivation of conformal Ward identities for these correlators

Abstract

We analyse the 3-point CFT correlators involving non-conserved spinning operators in momentum space. We derive a general expression for the conformal Ward identities defining the 3-point functions involving two generic spin $s$ non-conserved operators and a spin 1 conserved current. We give explicit expressions for the 3-point function when the two non-conserved operators have spins 1 and 2 and generic conformal dimensions. We also systematically analyse the divergences appearing in these 3-point functions when the conformal dimensions of the two non-conserved operators coincide.