Conformal Anomalies and the Gravitational Effective Action: The $TJJ$ Correlator for a Dirac Fermion

TL;DR

This paper calculates the contributions of a virtual Dirac fermion to the gravitational effective action related to conformal anomalies, focusing on the $TJJ$ correlator in linearized gravity.

Contribution

It provides a detailed computation of the $TJJ$ correlator for a Dirac fermion in gravity, linking conformal anomalies to the effective action in perturbation theory.

Findings

Derived the off-shell gauge-gauge-graviton vertex.

Expressed the anomalous effective action in the inverse fermion mass.

Connected the $TJJ$ correlator to conformal anomaly generation.

Abstract

We compute in linearized gravity all the contributions to the gravitational effective action due to a virtual Dirac fermion, related to the conformal anomaly. This requires, in perturbation theory, the identification of the gauge-gauge-graviton vertex off mass shell, involving the correlator of the energy-momentum tensor and two vector currents ($TJJ$), which is responsible for the generation of the gauge contributions to the conformal anomaly in gravity. We also present the anomalous effective action in the inverse mass of the fermion as in the Euler-Heisenberg case.