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Path integral measure and RG equations for gravity
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abstract
Considering the Einstein-Hilbert truncation for the running action in (euclidean) quantum gravity, we derive the renormalization group equations for the cosmological and Newton constant. We find that these equations admit only the Gaussian fixed point with a UV-attractive and a UV-repulsive eigendirection, and that there is no sign of the non-trivial UV-attractive fixed point of the asymptotic safety scenario. Crucial to our analysis is a careful treatment of the measure in the path integral that defines the running action and a proper introduction of the physical running scale $k$. We also show why and how in usual implementations of the RG equations the aforementioned UV-attractive fixed point is generated.
Forward citations
Cited by 3 Pith papers
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Quantum gravity and spectral running cutoff
Spectral hard and smooth cutoffs on the covariant Laplacian yield Einstein-Hilbert RG flows with a non-Gaussian UV-attractive fixed point, supporting asymptotic safety.
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Gravity and the Higgs boson mass
For a scalar field on a sphere, the Fradkin-Vilkovisky measure combined with an on-shell cutoff identification converts the famous quadratic mass divergence into a logarithmic one.
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Diffeomorphism invariance of the effective gravitational action
A careful calculation shows that the Fradkin-Vilkovisky path integral measure is diffeomorphism invariant, while the Fujikawa measure is not.
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