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 C2 invariant and the Euler (Gauss–Bonnet) invariant E4 can only be achieved for N-extended supergravity multiplets with N⩾5, as well as for M theory compactified to four dimensions. Although there remain open questions, in particular concerning the true significance of conformal anomalies in non-conformal theories, as well as their possible gauge dependence for spin s⩾32, these cancellations suggest a hidden conformal structure of unknown type in these theories.
Highlights
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
In this Letter, we study the effect of conformal anomalies on low energy gravitational physics
While the effect of the non-anomalous part of the non-local effective action on Einstein’s equations for any matter coupling is completely negligible away from the Planck regime, due to the powers of lPl that come with higher order curvature and other quantum corrections, we will here argue that the anomalous part Γanom[g, φ] of the non-local effective action, which is responsible for the conformal anomaly via formula (3) below, is relevant for the quantised theory, but could affect classical low energy processes in observable ways, for instance by exciting longitudinal gravitational degrees of freedom
Summary
Meissner and Hermann Nicolai2 1Faculty of Physics, University of Warsaw ul. 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 imposes strong restrictions on the field content of possible extensions of Einstein’s theory: all viable theories should have vanishing conformal anomalies. We show that a complete cancellation of conformal anomalies in D = 4 for both the C2 invariant and the Euler (Gauss-Bonnet) invariant E4 can only be achieved for N -extended supergravities with N 5, as well as for M theory compactified to four dimensions
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