More evidence for asymptotic safety (Saueressig, Machado, Benedetti)

[marcus]

http://arxiv.org/abs/0901.2984
Asymptotic safety in higher-derivative gravity
Dario Benedetti, Pedro F. Machado, Frank Saueressig
4 pages
(Submitted on 20 Jan 2009)
"We study the non-perturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The beta-functions give rise to a non-trivial ultraviolet fixed point with three UV-attractive and one UV-repulsive eigendirections, substantiating previous evidence that gravity is asymptotically safe. We argue that asymptotic safety also resolves the unitarity problem typically haunting higher-derivative gravity theories."

 

[marcus]

Until recently the three authors were all at Utrecht. We know of Benedetti and Machado as Loll PhD students, the former now has a postdoc position at Perimeter. Saueressig has co-authored several papers with Martin Reuter, one of the main proponents of asymptotic safety (ASQG). After several years as postdoc at the Utrecht ITP, he has moved to the Saclay center for theoretical physics near Versailles, France. Saclay is few kilometers out in the country southwest of Paris.

While a Loll PhD student, Machado has co-authored ASQG research with Saueressig. There is some interesting linkage between Asymptotic Safety and Loll's Causal Dynamical Triangulations QG. Both predict that the dimensionality of spacetime decreases from 4D down to near 2D as Planck scale is approached. Space and spacetime look smooth and normal at large scale but become fractal at microscopic scale.

This was the subject of a 2008 paper by Dario Benedetti, which we discussed here at PF. He identified a more general class of models which should have this microscopic fractal behavior. Although CDT and ASQG are formally and methodologically quite different, there seems to be some commonality of interest and crossover of people between the two research programs.

This quote from the introduction of the present paper gives a nice perspective on ASQG:

==excerpt==
Recently, the questionof unitarity and renormalizability has received renewed attention due to mounting evidence in favor of the non-perturbative
renormalizability, or asymptotic safety (AS), of gravity [9–11]. In this scenario, the ultraviolet (UV) behavior of the theory is controlled by a non-Gaussian fixed point (NGFP) of the renormalization group flow, with a finite number of UV-attractive (relevant) directions. This fixed point is
supposed to provide the theory with a continuum limit which is predictive and safe from divergences.
...
...
Since higher-derivative terms are expected to play a role at the NGFP, the question of unitarity has to be addressed. In order to do so it is necessary to investigate the non-perturbative RG flow associated with [certain] tensor structures... which had been avoided up to now for technical reasons. In this letter, we present for the first time non-perturbative results on such theories, by use of the FRGE. Our main result is the existence of a NGFP with three UV-attractive and one UV-repulsive eigen directions. This NGFP realizes a mechanism for the removal of the poltergeists from the spectrum of the theory, and thus provides a strong indication that asymptotically safe quantum gravity is actually unitary.
==endquote==

 

[Entropia]

I find this study by Benedetti, Machado, and Saueressig to be a significant contribution to the understanding of asymptotic safety in higher-derivative gravity theories. The use of functional renormalization group techniques allows for a non-perturbative analysis, providing a more complete and accurate picture of the renormalization group flow. The identification of a non-trivial ultraviolet fixed point with both attractive and repulsive directions further supports the idea that gravity may indeed be asymptotically safe.

This study also addresses the long-standing issue of unitarity in higher-derivative gravity theories. The fact that asymptotic safety resolves this problem is a promising indication that this approach may hold the key to a more complete and consistent theory of gravity.

However, it is important to note that this study is still in the early stages and further research and experimentation is needed to fully confirm the existence of asymptotic safety in higher-derivative gravity. Nevertheless, this work provides valuable evidence and insights that will undoubtedly inform and guide future studies in this area.