Conformal Anomalies and Gravitational Waves

TL;DR

This paper explores how conformal anomalies in gravitational theories can modify Einstein's equations and discusses the constraints these anomalies impose on viable theories, highlighting supergravity and M-theory as anomaly-free options.

Contribution

It demonstrates that canceling conformal anomalies in four-dimensional theories requires extended supergravities with N≥5 or M-theory compactifications, linking anomaly cancellation to specific high-energy theories.

Findings

Conformal anomalies can produce observable effects in gravity.

No anomalies observed constrains possible extensions of Einstein's theory.

Anomaly cancellation occurs only in certain supergravity theories and M-theory.

Abstract

We argue that the presence of conformal anomalies in gravitational theories can lead to observable modifications to Einstein's equations via the induced anomalous effective actions, whose non-localities can overwhelm the smallness of the Planck scale. The fact that no such effects have been seen in recent 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. We then show 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 supergravities with $N \geq 5$, as well as for M theory compactified to four dimensions.