Non-Abelian and Type-A Conformal Anomalies from Euler Descent

TL;DR

This paper classifies non-Abelian conformal anomalies in even dimensions using descent methods, relates them to Weyl anomalies, and discusses implications for anomaly inflow and effective actions.

Contribution

It introduces a classification of non-Abelian conformal anomalies via Euler descent, linking them to Weyl anomalies and extending anomaly inflow and matching frameworks.

Findings

Classified non-Abelian conformal anomalies using Euler invariant polynomials.

Connected non-Abelian anomalies to type-A Weyl anomalies through cocycle projections.

Constructed a 4d dilaton effective action matching the full conformal anomaly.

Abstract

We classify the non-Abelian anomaly of the Euclidean conformal group $SO(2n+1,1)$ in $2n$ dimensions via Stora-Zumino descent from its Euler invariant polynomial in $2n+2$ dimensions. In this way, we place the conformal anomaly on the same footing as ordinary perturbative 't Hooft anomalies. We also explore the relation of the non-Abelian anomaly to the known \textit{type-A Weyl anomaly}, which involves projecting into a Weyl cocycle. We discuss implications for anomaly inflow, and 't Hooft anomaly matching for the full conformal group with a Wess-Zumino-Witten term. In 4d, this enables the construction of a dilaton effective action matching the full non-Abelian $SO(5,1)$ conformal anomaly.