https://doi.org/10.1140/epjc/s10052-026-15733-w
Regular Article - Theoretical Physics
The effective field theory of the gravitational functional measure
1
Departamento de Física, Universidade Federal do Paraná, Rua Cel. Francisco Heráclito dos Santos, 100, 81531-980, Curitiba, PR, Brazil
2
SISSA, via Bonomea 265, 34136, Trieste, Italy
a
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Received:
9
February
2026
Accepted:
21
April
2026
Published online:
5
May
2026
Abstract
The gravitational path integral measure has been the subject of an increasing interest lately, and no conclusive answer yet exists for its correct form. In this paper, we adopt effective field theory techniques to shed light on this issue. We build the configuration-space metric as an energy expansion, including all possible terms that satisfy the underlying symmetries, and use it to define a Riemannian measure. We study the running of the free parameters that show up in this expansion at leading order, which corresponds to the DeWitt metric with parameter 
We show that a flat configuration space is excluded on unitarity grounds. Within the vacuum-sector normalization convention adopted here, the renormalization group flow in the DeWitt truncation exhibits a UV-attractive fixed point at 
This fixed point matches the value obtained by identifying DeWitt’s metric from the kinetic term of general relativity, but in our approach it arises without assuming that identification a priori, providing a renormalization group rationale for the standard choice.
© The Author(s) 2026
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