Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

By A. Codello, Roberto Percacci, Christoph Rahmede. 2008

545 citations recorded by the source corpus.

Abstract We review and extend in several directions recent results on the “asymptotic safety” approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a type of Wilsonian renormalization group equation. We begin by discussing various cutoff schemes, i.e. ways of implementing the Wilsonian cutoff procedure. We compare the beta functions of the gravitational couplings obtained with different schemes, studying first the contribution of matter fields and then the so-called Einstein–Hilbert truncation, where only the cosmological constant and Newton’s constant are retained. In this context we make connection with old results, in particular we reproduce the results of the epsilon expansion and the perturbative one-loop divergences. We then apply the Renormalization Group to higher derivative gravity. In the case of a general action quadratic in curvature we recover, within certain approximations, the known asymptotic freedom of the four-derivative terms, while Newton’s constant and of the cosmological constant have a nontrivial fixed point. In the case of actions that are polynomials in the scalar curvature of degree up to eight we find that the theory has a fixed point with three UV-attractive directions, so that the requirement of having a continuum limit constrains the couplings to lie in a three-dimensional subspace, whose equation is explicitly given. We emphasize throughout the difference between scheme-dependent and scheme-independent results, and provide several examples of the fact that only dimensionless couplings can have “universal” behavior.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b0d044ec25c6a70c5d5f3746584108f67be2534e

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In Astronomy and Astrophysics

1. R. Loll
2. J. Jurkiewicz
3. Martin Reuter
4. A. Eichhorn
5. J. Ambjørn
6. Jan M. Pawlowski
7. U. Harst
8. A. Goerlich

In Nuclear and High Energy Physics

1. A. Eichhorn
2. R. Loll
3. J. Jurkiewicz
4. Martin Reuter
5. W. Metzner
6. M. Tissier
7. L. Canet
8. N. Dupuis

In Statistical and Nonlinear Physics

1. R. Loll
2. J. Jurkiewicz
3. Martin Reuter
4. A. Eichhorn
5. J. Ambjørn
6. Jan M. Pawlowski
7. U. Harst
8. A. Goerlich

Citations in the corpus

• Nonperturbative quantum de Sitter universe (2008, background): “We also provide evidence that it may be possible to penetrate to the sub-Planckian regime, where the Planck length is large compared to the lattice spacing of the underlying regularization of geometry.”
• QED coupled to QEG (2011, background): “that dim SUV stabilized at s = 3 when the degree of the polynomial was increased [ 31 ].”
• The nonperturbative functional renormalization group and its applications (2020, background): “Figure 27: Real part of critical exponents sorted from most relevant towards irrelevant from the following references in single-metric calculations: 1 = [1071], 2=[1077], 3=[1124],4 =[1056], 5=[1072], 6=[1081], 7=[1086], 8=[1143].”
• Asymptotic safety in the f(R) approximation (2012, methodology): “Returning to the earlier forms of the f(R) approximation [15, 16], we have already seen that their choice of cutoff resulted in fixed singular points which in turn ruled out the existence of any global smooth fixed point solutions.”