Abstract
We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make nonlocal loop correction terms diffeomorphism invariant. Specifically, in a conformally flat spacetime , we find that effective actions are described in terms of momentum squared expressed as a physical for measured by the flat metric, which recalls the relationship between physical momentum and comoving momentum in cosmology. It is confirmed by calculating the effective action of QED in such a curved spacetime at the 3-loop level using dimensional regularization. The same applies to the case of QCD, in which we show that the effective action can be summarized in the form of the reciprocal of a running coupling constant squared described by the physical momentum. We also see that the same holds for renormalizable quantum conformal gravity and that conformal anomalies are indispensable for formulating the theory.
- Received 18 October 2020
- Accepted 10 November 2020
DOI:https://doi.org/10.1103/PhysRevD.102.125005
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Published by the American Physical Society