Covariantly Constant Anomalies on Conformal Manifolds

TL;DR

This paper investigates the covariant properties of type-B Weyl anomalies in conformal field theories, demonstrating that these anomalies are covariantly constant on conformal manifolds due to the Wess-Zumino consistency condition.

Contribution

It establishes that Weyl anomalies depend covariantly on exactly marginal couplings and are covariantly constant, extending the understanding to cases with spontaneously broken conformal symmetry.

Findings

Anomalies are covariantly constant on conformal manifolds.

The covariant anomaly functional is studied in several examples.

The result applies even when conformal symmetry is spontaneously broken.

Abstract

Operators with integer scaling dimensions in even-dimensional conformal field theories exhibit well-known type-B Weyl anomalies. In general, these anomalies depend non-trivially on exactly marginal couplings. We study the corresponding fully covariantised anomaly functional on conformal manifolds in several examples. We show that a natural consequence of the Wess-Zumino consistency condition is that the anomalies are covariantly constant with respect to the exactly marginal couplings. The argument is general and applies even when the conformal symmetry is spontaneously broken on moduli spaces of vacua.