Conformal Symmetry and the Three Point Function for the Gravitational Axial Anomaly

TL;DR

This paper calculates the two-loop contribution to the gravitational axial anomaly in a massless Abelian Higgs model, revealing non-vanishing effects due to conformal properties and tensor structures.

Contribution

It provides the first radiative calculation of the gravitational axial anomaly at two loops using conformal symmetry in coordinate space.

Findings

Two-loop contribution to the anomaly does not vanish.

Conformal properties facilitate the calculation in coordinate space.

Presence of two independent tensor structures affects the anomaly.

Abstract

This work presents a first study of a radiative calculation for the gravitational axial anomaly in the massless Abelian Higgs model. The two loop contribution to the anomalous correlation function of one axial current and two energy-momentum tensors, <A_alpha(z) T_\mu\nu(y) T_\rho\sigma(x)>, is computed at an order that involves only internal matter fields. Conformal properties of massless field theories are used in order to perform the Feynman diagram calculations in the coordinate space representation. The two loop contribution is found not to vanish, due to the presence of two independent tensor structures in the anomalous correlator.