Abstract
We study the renormalization group flow of gravity coupled to scalar matter using functional renormalization group techniques. The novel feature is the inclusion of higher-derivative terms in the scalar propagator. Such terms give rise to Ostrogradski ghosts which signal an instability of the system and are therefore dangerous for the consistency of the theory. Since it is expected that such terms are generated dynamically by the renormalization group flow they provide a potential threat when constructing a theory of quantum gravity based on Asymptotic Safety. Our work then establishes the following picture: upon incorporating higher-derivative terms in the scalar propagator the flow of the gravity-matter system possesses a fixed point structure suitable for Asymptotic Safety. This structure includes an interacting renormalization group fixed point where the Ostrogradski ghosts acquire an infinite mass and decouple from the system. Tracing the flow towards the infrared it is found that there is a subset of complete renormalization group trajectories which lead to stable renormalized propagators. This subset is in one-to-one correspondence to the complete renormalization group trajectories obtained in computations which do not keep track of the higher-derivative terms. Thus our asymptotically safe gravity-matter systems are not haunted by Ostrogradski ghosts.
Highlights
It has been shown that this fixed point is robust under the inclusion of the two-loop counterterm [14] and is connected to a classical regime through a crossover [15]
We study the renormalization group flow of gravity coupled to scalar matter using functional renormalization group techniques
Since it is expected that such terms are generated dynamically by the renormalization group flow they provide a potential threat when constructing a theory of quantum gravity based on Asymptotic Safety
Summary
We start by briefly reviewing the classical Ostrogradski instability and its loopholes, mainly following the expositions [72, 73]. One way for curing the Ostrogradski instability at the classical level is to lift the condition of non-degeneracy In this case the higher-order time derivatives are removed by either combining them into total derivatives or using a gauge symmetry. When assessing the stability of a higher-derivative theory at the quantum level, the situation becomes even more involved In this case the dressed propagator of the theory can be obtained from the effective action Γ and one expects that for a stable theory this propagator does not give rise to Ostrogradski ghosts. At finite values of k it is expected that the process of integrating out quantum fluctuations mode-by-mode will generate higher-order derivative terms in the intermediate description This does not signal the sickness of the theory, as its degrees of freedom should be read off from the dressed propagator. This generalization is beyond the present work though, so we will not discuss this case in detail
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