AsymSafe QG sees a numerical breakthrough (Benedetti, Groh, Machado, Saueressig)

[marcus]

http://arxiv.org/abs/1012.3081
The Universal RG Machine
Dario Benedetti, Kai Groh, Pedro F. Machado, Frank Saueressig
38 pages
(Submitted on 14 Dec 2010)
"Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in a given background quantity specified by the approximation scheme. The method is based on off-diagonal heat-kernel techniques and can be implemented on a computer algebra system, opening access to complex computations in, e.g., Gravity or Yang-Mills theory. In a first illustrative example, we re-derive the gravitational beta-functions of the Einstein-Hilbert truncation, demonstrating their background-independence. As an additional result, the heat-kernel coefficients for transverse vectors and transverse-traceless symmetric matrices are computed to second order in the curvature."

This has considerable importance. It makes the Asymptotic Safe QG approach much more viable and opens the way to rapid progress.

 

[Coin]

The jargon here is a little over my head...

Does this allow you to calculate things in QG you could not otherwise, or is this about bringing AsymSafe up to speed with other QG approaches?

Does using this approach require you to assume certain things about the nature of QG? For example, do you have to assume a QG fixed point exists?

 

[marcus]

I wasn't clear. Maybe someone else would like to give their perspective on it---and that might be clearer to you than what I'm going to say.

Here's what I think. It has always been hard to check that the UV fixed point exists because one could only handle expressions with a finite number of terms. Here is a machine algorithm. It will make the business of checking and determining the UV fixed point much easier (if it in fact exists!)

It has always been a worry whether the AS approach was BACKGROUND INDEPENDENT. Reuter has stubbornly devoted paper after unsatisfactory paper to this. Because you need a background metric to get started with. Now it looks like these people have finally shown background independence conclusively.

AS gravity by itself is not a quantum theory of gravity. Sorry for giving that impression. It is a way of treating classical gravity so that it is in effect renormalizable (predictive after a finite number of constants are set) and I think of it as potentially leading to a quantum theory of gravity. It is premature to talk about AS QG, but I tend to do that---think of it as one of several competing QG approaches.

Here's a video talk on AS by Steven Weinberg, given earlier this year:
https://mediamatrix.tamu.edu/streams/327756/PHYS_Strings_2010_3-18-10C

Percacci's website:
http://www.percacci.it/roberto/physics/as/index.html

Again, I'd like to hear some other people's perspectives on this.

 

[atyy]

There are 2 distinct ideas in AS.

1) Is there a fixed point? If there is, then it is a class of theories of quantum gravity.

2) Do all roads lead to the fixed point, or only some. If all, then we have too many(!) theories of quantum gravity. If some, then we recover predictability.