1. What are the contributions in "Critical exponents in quantum einstein gravity" ?
It is shown that the exponent provides a minimal sensitivity to the parameters of the regulator which correspond to the Litim ’ s regulator.
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Critical exponents in quantum Einstein gravity
TL;DR: In this article, the quantum Einstein gravity is treated by the functional renormalization group method using the Einstein-Hilbert action and the ultraviolet non-Gaussian fixed point is determined and its corresponding exponent of the correlation length is calculated for a wide range of regulators.
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Abstract: The quantum Einstein gravity is treated by the functional renormalization group method using the Einstein-Hilbert action. The ultraviolet non-Gaussian fixed point is determined and its corresponding exponent of the correlation length is calculated for a wide range of regulators. It is shown that the exponent provides a minimal sensitivity to the parameters of the regulator which correspond to the Litim's regulator.
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Figures
FIG. 2. The phase structure of QEG is shown for css regulator with the parameters s1 ¼ s2 ¼ b ¼ 1. The grey points denote the critical points. The thick line represents the separatrix. 
FIG. 5. The power-law scaling of the correlation length ξ is shown for various parameters of the css regulator, we chose s1 ¼ b ¼ 1. From the negative slope of the logarithmic plot we obtained that ν ¼ 1=2. 
TABLE I. The summary of the critical exponent ν and the anomalous dimensions η at the various fixed points of QEG. 
FIG. 6. The anomalous dimension η is plotted as the function of the scale. In the vicinity of the fixed points the η shows different scaling behaviors. We chose s1 ¼ s2 ¼ b¼ 1 for the css regulator. 
FIG. 1. The exponent ν is calculated for 2 and 4 couplings and shown by the curves at the bottom and at the top, respectively. The Litim’s regulator gives the extremal exponent in both cases at the point of the crossing of the grey lines. 
FIG. 4. The exponent 1=ν is calculated for various values of parameters of the css regulator. In the inset the different curves correspond to different values of s2 ¼ 1, 5, 10, 20, 50, 100, 200, 500, 1000, increasing from below. There we chose b ¼ 1.
Citations
The nonperturbative functional renormalization group and its applications
N. Dupuis,Léonie Canet,Astrid Eichhorn,Astrid Eichhorn,W. Metzner,Jan M. Pawlowski,Matthieu Tissier,Nicolás Wschebor +7 more
TL;DR: The nonperturbative functional renormalization-group (FRG) approach as discussed by the authors is a modern implementation of Wilson's RG, which allows one to set up nonperturative approximation schemes that go beyond the standard perturbative RG approaches.
351
The nonperturbative functional renormalization group and its applications
N. Dupuis,Léonie Canet,Astrid Eichhorn,Astrid Eichhorn,W. Metzner,Jan M. Pawlowski,Matthieu Tissier,Nicolás Wschebor +7 more
TL;DR: The nonperturbative functional renormalization-group (FRG) approach as discussed by the authors is a modern implementation of Wilson's RG, which allows one to set up nonperturative approximation schemes that go beyond the standard perturbative RG approaches.
267
Critical reflections on asymptotically safe gravity
Alfio Bonanno,Astrid Eichhorn,Astrid Eichhorn,Holger Gies,Jan M. Pawlowski,Roberto Percacci,Martin Reuter,Frank Saueressig,Gian Paolo Vacca +8 more
TL;DR: Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity as discussed by the authors, and significant progress on this program has led to a first characterization of the Reuter fixed point.
Quantum gravity on foliated spacetimes: Asymptotically safe and sound
TL;DR: In this paper, a functional renormalization group equation adapted to the ADM-formalism was used for evaluating the gravitational renormalisation group flow on a cosmological Friedmann-Robertson-Walker background.
164
Towards apparent convergence in asymptotically safe quantum gravity
TL;DR: Christiansen et al. as mentioned in this paper presented a closed flow equation for the graviton propagator, where all vertices and propagators involved are computed from their own flows, and showed the apparent convergence of the systematic vertex expansion.
References
Non-perturbative renormalization flow in quantum field theory and statistical physics
TL;DR: In this paper, the use of exact renormalization group equation in quantum field theory and statistical physics is reviewed. But the authors focus on the second-order phase transition and the critical behavior of polymer chains, and do not consider the non-perturbative solutions of the coarse-grained free energy.
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TL;DR: In this paper, a scale-dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow and satisfies modified Becchi-Rouet-Stora Ward identities.
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Optimized renormalization group flows
TL;DR: In this article, the exact renormalization group (ERG) flows were studied and the convergence of approximate solutions towards the physical theory was optimized by appropriate choices of the regularization.