Assymptotic Safety (to nonperturbatively renormalize gravity)

[marcus]

Asymptotic Safety (to nonperturbatively renormalize gravity)

the idea is to get a predictive theory, where you only have to specify the values of a finite number of physically meaningful parameters---experimentally determined--and from there on your theory predicts stuff.

and it is NOT based on a perturbative powerseries expansion with "first order, second order" etc. terms. so the usual talk about diagrams for calculating terms in the series, one-loop and two-loop etc... that usual talk doesn't apply in this context. Because it is a different kind of renormalization, which Reuter and his bunch calle NONperturbative.

The idea was originally due to Steven Weinberg who tried it back in 1976-1979 and Weinberg called it ASYMPTOTIC SAFETY.

Basically what that means is you find a fixed point in the renormalization flow that allows your theory to be predictive after some finite number of parameters are specified.

Judging from Percacci's recent work it looks like the number of parameters is turning out to be something like THREE.

WELL NOW IT LOOKS LIKE THERE IS GOING TO BE A PERCACCI CHAPTER IN ORITI'S BOOK

http://arxiv.org/abs/0709.3851
Asymptotic Safety
R. Percacci
To appear in "Approaches to Quantum Gravity: Towards a New Understanding of Space, Time and Matter", ed. D. Oriti, Cambridge University Press
(Submitted on 24 Sep 2007)

"Asymptotic safety is a set of conditions, based on the existence of a nontrivial fixed point for the renormalization group flow, which would make a quantum field theory consistent up to arbitrarily high energies. After introducing the basic ideas of this approach, I review the present evidence in favor of an asymptotically safe quantum field theory of gravity".

 

[marcus]

There is something interesting on page 24-25 of that Percacci paper, towards the end of the Q/A section

==quote==
Q: You mention that the results of the Exact Renormalization Group (ERG) seem to point out that spacetime structure cannot be described in terms of a single metric [that works] for any momentum scale. How would one notice, in the RG approach, that it cannot be described by a metric field at all, but that a description in terms of connections or even a non-local one would be more appropriate, say, at the Planck scale?

A: I do in fact expect that an independent connection will manifest itself at the Planck scale, as I have indicated in my answer to another question, though I don’t think that this will be forced upon us by the ERG.

The scale-dependence of the metric could manifest itself as violations of the equivalence principle, or perhaps as Lorentz-invariance violations or deformations of the Lorentz group. There is much work to be done to understand this type of phenomenology. Even more radically, it is possible that gravity is just the “low energy” manifestation of some completely different physics, as suggested in the article by Dreyer. This would probably imply a failure of the asymptotic safety programme, for example a failure to find a fixed point when certain couplings are considered.

Q: Can you please comment on possibility of extending...
==endquote==

What I like is the completeness of Percacci's thought. He has already thought about how THE ASYMPTOTIC SAFETY PROGRAM CAN FAIL and how that could show up. Personally I do not expect it to fail, and I gather that neither does Percacci! But I respect it when things are falsifiable and subject to refutation by various kinds of checks.

In this passage notice that he does not even have to consider ways the program could fail---the question was not directed at that. He adds that to his answer for the laudable purpose of completeness.

 

[Entropia]

Asymptotic Safety is a promising approach to nonperturbatively renormalize gravity and potentially provide a predictive theory. The concept was originally proposed by Steven Weinberg in 1976-1979 and has been further developed by researchers such as Reuter and Percacci. The key idea is to find a fixed point in the renormalization flow that allows the theory to be predictive after a finite number of physically meaningful parameters are specified.

This approach differs from traditional perturbative methods, which rely on a power series expansion and calculations of diagrams. Instead, Asymptotic Safety focuses on a nonperturbative renormalization flow and the existence of a fixed point, which can lead to a finite number of parameters being able to predict the behavior of the theory at high energies.

Recent work by Percacci has shown that the number of parameters in an asymptotically safe quantum field theory of gravity may be as low as three. This is a promising development and suggests that the theory may be able to make accurate predictions with a minimal number of parameters.

Overall, Asymptotic Safety offers a new perspective on nonperturbative renormalization in gravity and has the potential to provide a predictive theory that is consistent up to arbitrarily high energies. It is an exciting area of research and we look forward to seeing further developments in this field.