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marcus

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This paper may be slow to get the attention it merits because of its density and length. I have just printed out pages 1-5, and pages 64-70, from the introduction and conclusion sections, to chew over at leisure

http://arxiv.org/abs/0805.2909

Alessandro Codello, Roberto Percacci, Christoph Rahmede

86 pages, 13 figures

(Submitted on 19 May 2008)

"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 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."

This quarter (April - June 2008) has been unusually productive of quantum gravity research and there are more good papers out there than one can properly take in. I may be forced to lay this one aside for a few days. Perhaps someone else may take an interest in it and discuss it. If not, I'll get around to it later. I think it is a signficant paper because it provides additional evidence that gravity is actually renormalizable (in a certain special sense*), due to the existence of a fixed point of the renormalization group flow.

*which some may object to calling renormalizability

http://arxiv.org/abs/0805.2909

**Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation**Alessandro Codello, Roberto Percacci, Christoph Rahmede

86 pages, 13 figures

(Submitted on 19 May 2008)

"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 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."

This quarter (April - June 2008) has been unusually productive of quantum gravity research and there are more good papers out there than one can properly take in. I may be forced to lay this one aside for a few days. Perhaps someone else may take an interest in it and discuss it. If not, I'll get around to it later. I think it is a signficant paper because it provides additional evidence that gravity is actually renormalizable (in a certain special sense*), due to the existence of a fixed point of the renormalization group flow.

*which some may object to calling renormalizability

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