Is conformal symmetry really anomalous? (1709.00330v1)

Abstract: The conformal anomaly (also known as the stress-energy trace anomaly) of an interacting quantum theory, associated with violation of Weyl (conformal) symmetry by quantum effects, can be amended if one endows the theory with a dilatation current coupled to a vector field that is the gauge connection of local Weyl symmetry transformations. The natural candidate for this Weyl connection is the trace of the geometric torsion tensor, especially if one recalls that pure (Cartan-Einstein) gravity with torsion is conformal. We first point out that both canonical and path integral quantisation respect Weyl symmetry. The only way quantum effects can violate conformal symmetry is by the process of regularization. However, if one calculates an effective action from a conformally invariant classical theory by using a regularisation procedure that is conform with Weyl symmetry, then the conformal Ward identities will be satisfied. In this sense Weyl symmetry is not broken by quantum effects. This work suggests that Weyl symmetry can be treated on equal footing with gauge symmetries and gravity, for which an infinite set of Ward identities guarantees that they remain unbroken by quantum effects.