Conformal Symmetry and the Chiral Anomaly

TL;DR

This paper calculates two-loop contributions to three-current correlators in massless field theories using conformal symmetry, confirming the Adler-Bardeen theorem by showing these contributions vanish across various models.

Contribution

It extends a conformal method to compute two-loop anomalies in different gauge theories, demonstrating their total cancellation and confirming theoretical predictions.

Findings

Two-loop contributions to gauge current correlators vanish.

The method confirms the Adler-Bardeen theorem.

The approach applies to supersymmetric gauge theories.

Abstract

Two-loop contributions to the anomalous correlation function <J_mu(x)J_nu(y)J_rho(z)> of three chiral currents are calculated by a method based on the conformal properties of massless field theories. The method was previously applied to virtual photon diagrams in quantum electrodynamics, and it is extended here to diagrams with scalars and chiral spinors in the abelian Higgs model and in the SU(3)xSU(2)xU(1) standard model. In each case there are nonvanishing contributions to the gauge current correlator from self-energy insertions, vertex insertions and nonplanar diagrams, but their sum exactly vanishes. The two-loop contribution to the anomaly therefore also vanishes, in agreement with the Adler-Bardeen theorem. An application of the method to the correlator <R_mu(x)R_nu(y)K_rho(z)> of the R and Konishi axial currents in supersymmetric gauge theories which was reported in hep-th/9608125 is discussed here. The net two-loop contribution to this correlator also vanishes.