A functional renormalization group equation for foliated spacetimes

Rechenberger, Stefan; Saueressig, Frank

doi:10.1007/jhep03(2013)010

Cited by 80 publications

(73 citation statements)

References 102 publications

(169 reference statements)

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“…In particular, there is a very good agreement with the critical exponents obtained for foliated spacetime via the Matsubara formalism [88,89]. Thus it is highly conceivable that the AS-NGFP seen in these computations is the one underlying Asymptotic Safety.…”

Section: Fixed Points and Universality Classessupporting

confidence: 72%

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Quantum gravity on foliated spacetimes: Asymptotically safe and sound

2017

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Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the non-Gaussian fixed points characteristic for Asymptotic Safety the setting exhibits a second family of non-Gaussian fixed points with a positive Newton's constant and real critical exponents. The presence of these new fixed points alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the -expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.

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Section: Fixed Points and Universality Classessupporting

confidence: 72%

“…In the present investigation we use the formulation of the FRGE where the gravitational degrees of freedom are carried by the ADM-fields [88,89]. In this case, the (Euclidean) spacetime metric is decomposed according to…”

Section: Functional Renormalizationmentioning

confidence: 99%

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

2017

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“…This program has been initiated in [43,44] and turns out to be crucial for understanding the background covariance of Asymptotic Safety [45,46], precision computations elucidating the structure of the NGFP [47][48][49] and establishing monotonicity properties of the gravitational RG flow expected from standard RG arguments [50]. The dependence of the NGFP on the signature of the metric was first investigated in [51], showing that the Asymptotic Safety mechanism is realized independently of the signature of the metric [52]. Asymptotic Safety has also been showed to play a significant role in understanding of the phase diagram of the anisotropic theories of gravity, dubbed Hořava-Lifshitz gravity [53].…”

Section: Asymptotic Safety: a Primermentioning

confidence: 99%

“…For the remainder of this section we then study the properties of the flow implied by (52). For this purpose we set d = 4 and chose the optimized regulator [93] ϱ…”

Section: The Einstein-hilbert Truncationmentioning

confidence: 99%

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

2015

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a b s t r a c tWe construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the structure of the new flow equation is considerably simpler than the standard Quantum Einstein Gravity construction since only transverse-traceless and trace part of the metric fluctuations propagate in loops. The geometric flow reproduces the phase-diagram of the Einstein-Hilbert truncation including the non-Gaussian fixed point essential for Asymptotic Safety. Extending the analysis to the polynomial f (R)-approximation establishes that this fixed point comes with similar properties as the one found in metric Quantum Einstein Gravity; in particular it possesses three UV-relevant directions and is stable with respect to deformations of the regulator functions by endomorphisms.

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“…Investigations of the gravitational RG flows based on the ADM-formalism [36,37], the Einstein-Cartan formalism [38][39][40][41] and the "tetrad…”

Section: Jhep08(2015)113mentioning

confidence: 99%

A proper fixed functional for four-dimensional Quantum Einstein Gravity

Demmel

Saueressig

Zanusso

2015

J. High Energ. Phys.

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103

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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 R 2 , 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.

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A functional renormalization group equation for foliated spacetimes

Cited by 80 publications

References 102 publications

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

A proper fixed functional for four-dimensional Quantum Einstein Gravity

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