Type-A Conformal Anomalies from Euler Descent

TL;DR

This work shows that the type-A conformal anomaly in $2n$ dimensions can be derived via Stora-Zumino descent from the Euler invariant of the group $SO(2n+1,1)$ in $2n+2$ dimensions, placing conformal anomalies on the same cohomological footing as perturbative ’t Hooft anomalies and enabling an anomaly inflow viewpoint. The construction yields a general formula for the Weyl-projected Euler descent, reproducing the familiar 2d and 4d type-A densities as special cases and naturally pairing the anomaly with a bulk Chern-Simons-type action. In 4d, the authors build a dilaton effective action realizing $SO(5,1)/ISO(4)$ nonlinearly, providing a concrete mechanism for anomaly matching along RG flows through a Wess-Zumino-Witten term. The results generalize to arbitrary $2n$ dimensions and open avenues for studying positivity bounds, $a$-theorem-like statements, and the full conformal anomaly structure beyond the traditional Riemannian background setting.

Abstract

We show that the type-A conformal anomaly in $2n$ dimensions follows from standard Stora-Zumino descent, starting from the Euler invariant polynomial for the Euclidean conformal group $SO(2n+1,1)$ in $6d$, thereby placing type-A anomalies on the same footing as ordinary perturbative t Hooft anomalies. 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 type-A $SO(5,1)$ conformal anomaly.