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 $$N \ge 5$$ .