Conformal anomaly actions for dilaton interactions

TL;DR

This paper explores the connection between the perturbative conformal anomaly signatures and effective dilaton actions in conformally invariant theories like QCD, revealing how anomaly-induced interactions are governed by fundamental symmetry relations.

Contribution

It demonstrates that the hierarchy of dilaton self-interactions is fully determined by the first four recurrence relations, generalizable to any even dimension.

Findings

Anomaly poles relate to Wess-Zumino dilaton actions.

Hierarchy of dilaton interactions is fixed by initial relations.

Results apply to all gauge-invariant sectors of the Standard Model.

Abstract

We discuss, in conformally invariant field theories such as QCD with massless fermions, a possible link between the perturbative signature of the conformal anomaly, in the form of anomaly poles of the 1-particle irreducible effective action, and its description in terms of Wess-Zumino actions with a dilaton. The two descriptions are expected to capture the UV and IR behaviour of the conformal anomaly, in terms of fundamental and effective degrees of freedom respectively, with the dilaton effective state appearing in a nonlinear realization. As in the chiral case, conformal anomalies seem to be related to the appearance of these effective interactions in the 1PI action in all the gauge-invariant sectors of the Standard Model. We show that, as a consequence of the underlying anomalous symmetry, the infinite hierarchy of recurrence relations involving self-interactions of the dilaton is entirely determined only by the first four of them. This relation can be generalized to any even space-time dimension.