Regularization of energy-momentum tensor correlators and parity-odd terms

TL;DR

This paper explores regularizing energy-momentum tensor correlators in conformal field theories, comparing coordinate and momentum space methods, and investigates parity-odd contributions and anomalies in 2d and 4d models.

Contribution

It introduces a momentum space regularization approach for energy-momentum correlators and analyzes parity-odd terms and anomalies in conformal field theories.

Findings

Consistent results for 2-point functions in 2d and 4d using different regularization methods.

Derived regularized trace and divergence of the energy-momentum tensor in a chiral fermion model.

Discussed the challenges of parity-odd trace anomaly in conformal field theories.

Abstract

We discuss the problem of regularizing correlators in conformal field theories. The only way to do it in coordinate space is to interpret them as distributions. Unfortunately except for the simplest cases we do not have tabulated mathematical results. The way out we pursue here is to go to momentum space and use Feynman diagram techniques and their regularization methods. We focus on the energy-momentum tensor correlators and, to gain insight, we compute and regularize 2-point functions in 2d with various techniques both in coordinate space and in momentum space, obtaining the same results. Then we do the same for 2-point functions in 4d. Finally we turn to 3-point function in 4d, and concentrate on the parity-odd part. We derive in particular the regularized trace and divergence of the energy-momentum tensor in a chiral fermion model. We discuss the problems related to the parity-odd trace anomaly.