Renormalization, Conformal Ward Identities and the Origin of a Conformal Anomaly Pole

TL;DR

This paper explores how conformal anomaly poles arise in conformal field theories, linking perturbative and non-perturbative approaches, and discusses their significance in topological materials and gauge theories.

Contribution

It demonstrates the generation of anomaly poles in the $TJJ$ correlator through dimensional renormalization and relates different form factor bases, highlighting their physical implications.

Findings

Anomaly poles are generated in the $TJJ$ correlator via dimensional renormalization.

The relation between $F$-basis and $A$-basis form factors clarifies the singular behavior.

Massless effective interactions from anomalies are relevant in topological insulators and gauge theories.

Abstract

We investigate the emergence of a conformal anomaly pole in conformal field theories in the case of the $TJJ$ correlator. We show how it comes to be generated in dimensional renormalization, using a basis of 13 form factors (the $F$-basis), where only one of them requires renormalization $(F_{13})$, extending previous studies. We then combine recent results on the structure of the non-perturbative solutions of the conformal Ward identities (CWI's) for the $TJJ$ in momentum space, expressed in terms of a minimal set of 4 form factors ($A-$ basis), with the properties of the $F$-basis, and show how the singular behaviour of the corresponding form factors in both basis can be related. The result proves the centrality of such massless effective interactions induced by the anomaly, which have recently found realization in solid state, in the theory of topological insulators and of Weyl semimetals. This pattern is confirmed in massless abelian and nonabelian theories (QED and QCD) investigated at one-loop.