Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions

TL;DR

This paper provides an algebraic framework for understanding Weyl anomalies in arbitrary dimensions, revealing their universal structure independent of regularization schemes.

Contribution

It introduces a purely algebraic approach to classify Weyl anomalies across all dimensions, advancing the theoretical understanding of conformal symmetry breaking.

Findings

Universal algebraic structure of Weyl anomalies identified

Applicable in arbitrary dimensions

Independent of regularization schemes

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.