Momentum space parity-odd CFT 3-point functions

TL;DR

This paper investigates the structure of parity-odd three-point functions involving scalars and conserved currents in conformal field theories within momentum space, employing conformal Ward identities and operator techniques.

Contribution

It introduces a method to determine the form of parity-odd 3-point functions in momentum space using conformal Ward identities and operator tools, including divergence regularization.

Findings

Explicit forms of parity-odd 3-point functions derived

Regularization and renormalization procedures detailed

Framework applicable to conformal field theories in momentum space

Abstract

We study the parity-odd sector of 3-point functions comprising of scalar operators and conserved currents in conformal field theories in momentum space. We use momentum space conformal Ward identities as well as spin-raising and weight-shifting operators to fix the form of these correlators. We discuss in detail the regularisation of divergences and their renormalisation using specific counter-terms.