Foundations of Physics

, Volume 48, Issue 10, pp 1150–1158 | Cite as

Non-local Effects of Conformal Anomaly

  • Krzysztof A. MeissnerEmail author
  • Hermann Nicolai
Part of the following topical collections:
  1. Black holes, Gravitational waves and Space Time Singularities


It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein’s equations. The fact that Einstein’s general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein’s theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in \(D=4\) for both the \(C^2\) invariant and the Euler (Gauss–Bonnet) invariant can only be achieved for N-extended supergravity multiplets with \(N \ge 5\).


Conformal anomaly Extended supergravities 



K.A.M. would like to thank the AEI for hospitality and support during this work; he was also partially supported by the Polish National Science Centre Grant DEC-2017/25/B/ST2/00165. H.N. would like to thank S. Kuzenko and P. Bouwknegt for hospitality at UWA in Perth and ANU in Canberra, respectively, while this work was underway, and A. Buonanno, M.J. Duff, J. Erdmenger, H. Godazgar, R. Kallosh, H. Osborn, A. Tseytlin and A. Schwimmer for discussions or correspondence. K.A.M. would like to thank R. Penrose for discussions in Czerwińsk and Oxford.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversity of WarsawWarsawPoland
  2. 2.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)PotsdamGermany

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