Exact Results in Quantum Theory

The presence of conformal anomalies in gravitational theories can lead to observable modifications to Einstein's equations via the induced anomalous effective actions. The fact that no such effects have been seen in cosmological or gravitational wave observations therefore imposes strong restrictions on the field content of possible extensions of Einstein's theory: all viable theories should have vanishing conformal anomalies. The 'miraculous' cancellation of conformal anomalies for N-extended supergravities will be discussed.