Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions

TL;DR

For the first time, a general, purely algebraic understanding of the universal structure of the Weyl anomalies is obtained, in arbitrary dimensions and independently of any regularization scheme.

Abstract

Conformally invariant massless field systems involving only dimensionless parameters are known to describe particle physics at very high energy. In the presence of an external gravitational field, the conformal symmetry may generalize to Weyl invariance. However, the latter symmetry no longer survives after quantization: A Weyl anomaly appears. In this Letter, a purely algebraic understanding of the universal structure of the Weyl anomalies is presented. The results hold in arbitrary dimensions and independently of any regularization scheme.