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Non-local Effects of Conformal Anomaly

Abstract

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 \(N \ge 5\).

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Notes

  1. We are grateful to M.J. Duff for correspondence on this point.

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Acknowledgements

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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Meissner, K.A., Nicolai, H. Non-local Effects of Conformal Anomaly. Found Phys 48, 1150–1158 (2018). https://doi.org/10.1007/s10701-018-0160-5

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Keywords

  • Conformal anomaly
  • Extended supergravities