Abstract
Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory’s renormalization group flow. In this work, we use the functional renormalization group equation for the effective average action to study the fixed point underlying Quantum Einstein Gravity at the functional level including an infinite number of scale-dependent coupling constants. We formulate a list of guiding principles underlying the construction of a partial differential equation encoding the scale-dependence of f(R)-gravity. We show that this equation admits a unique, globally well-defined fixed functional describing the non-Gaussian fixed point at the level of functions of the scalar curvature. This solution is constructed explicitly via a numerical double-shooting method. In the UV, this solution is in good agreement with results from polynomial expansions including a finite number of coupling constants, while it scales proportional to R2, dressed up with non-analytic terms, in the IR. We demonstrate that its structure is mainly governed by the conformal sector of the flow equation. The relation of our work to previous, partial constructions of similar scaling solutions is discussed.
Highlights
Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory’s renormalization group flow
We use the functional renormalization group equation for the effective average action to study the fixed point underlying Quantum Einstein Gravity at the functional level including an infinite number of scale-dependent coupling constants
We used the functional renormalization group equation for the effective average action Γk, (1.1), to establish the existence of a suitable fixed function in the realm of f (R)-truncations spanned by the ansatz (1.2)
Summary
The RG flow of any theory admits a GFP at which the theory itself becomes noninteracting. The NGFP has been put to test and proved robust to the inclusion of the problematic operators appearing in the perturbative counter-terms in Γk [21, 22], directly showing the feasibility of the program beyond perturbation theory Despite this fixed point being associated with an interacting quantum field theory in which the (background) Newton’s constant scales with an anomalous dimension ηN = −2, classical power-counting may still constitute a good ordering principle for identifying the relevant deformations of the fixed point as shown in [23,24,25,26]. This leads to the perhaps surprising conclusion that, at the level of finite-dimensional projections, the appearance of a NGFP in gravitational theories is rather commonplace instead of exceptional.
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