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Conformally invariant massless field systems involving only dimensionlessparameters are known to describe particle physics at very high energy. In thepresence of an external gravitational field, the conformal symmetry maygeneralize to Weyl invariance. However, the latter symmetry no longer survivesafter quantization: A Weyl anomaly appears. In this Letter, a purely algebraicunderstanding of the universal structure of the Weyl anomalies is presented.The results hold in arbitrary dimensions and independently of anyregularization scheme.

Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions