Abstract
We review the study of the scaling properties of geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the use of such operators and how they can be embedded in the effective average action formalism. We report the anomalous dimension of the geometric operators in the Einstein–Hilbert truncation via different approximations by considering simple extensions of previous studies.
Highlights
In the Asymptotic Safety (AS) scenario, gravity is quantized in a quantum field theoretic framework [1]
In [2] a functional renormalization group (FRG) flow equation for quantum gravity was derived in terms of the so-called effective average action (EAA) [3], which is a scale dependent generalization of the usual effective action
We emphasize that in a non-perturbative framework such as the FRG, such a procedure may in principle change rather drastically the numerical values of γσn with respect to those obtained in the following, which are based on a crude approximation scheme and vary over a significant range when comparing the results of Sections 4.1.1, 4.1.2, and 4.1.3
Summary
In the Asymptotic Safety (AS) scenario, gravity is quantized in a quantum field theoretic framework [1] In this approach a fundamental quantum field theory of gravity is defined thanks to the presence of an ultraviolet-attractive non-Gaussian fixed point with a finite number of relevant directions [1,2]. The gravitational extension of the EAA allows one to use this framework to investigate the presence of a suitable fixed point for the AS scenario for quantum gravity [2]. Even in the presence of a suitable fixed point, further effort is often needed to make contact with gravitational observables [52,53] The reason for this is that on top of the EAA, one needs to make contact with geometric operators such as the geodesic length.
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