• Open Access

Diffeomorphism invariance demands conformal anomalies

Ken-ji Hamada
Phys. Rev. D 102, 125005 – Published 1 December 2020

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 ds2=e2ϕ(dη2+dx2), we find that effective actions are described in terms of momentum squared expressed as a physical Q2=q2/e2ϕ for q2 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.

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  • Received 18 October 2020
  • Accepted 10 November 2020

DOI:https://doi.org/10.1103/PhysRevD.102.125005

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Ken-ji Hamada

  • Institute of Particle and Nuclear Studies, KEK, Tsukuba 305-0801, Japan and Department of Particle and Nuclear Physics, The Graduate University for Advanced Studies (SOKENDAI), Tsukuba 305-0801, Japan

Article Text

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Issue

Vol. 102, Iss. 12 — 15 December 2020

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