BeGroMaS: gravity was renormalizable after all, so why all the fuss?

[marcus]

Benedetti Groh Machado Saueressig have (what will probably turn out to be) a landmark paper where they show the Renormalization Group Flow treatment of gravity is background independent.

We already saw mounting evidence of a UV fixed point with finite dimensional attractive surface. The term often used is that gravity is non-perturbatively renormalizable because the theory is predictive to arbitrary high energy once a finite number (like 3) parameters are determined. The BGMS algorithm that they present in the paper will help confirm or falsify that.

The leading researchers involved (Weinberg Percacci Reuter...) refer to this as nonperturbative renormalizability because the theory cannot be developed by perturbing around flat space zero gravity---you have to shift over to the UV fixed point. Otherwise it behaves as you expect and does what a renormalizable theory is supposed to do.

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...
... 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."

 

[Careful]

Benedetti Groh Machado Saueressig have (what will probably turn out to be) a landmark paper where they show the Renormalization Group Flow treatment of gravity is background independent.

We already saw mounting evidence of a UV fixed point with finite dimensional attractive surface. The term often used is that gravity is non-perturbatively renormalizable because the theory is predictive to arbitrary high energy once a finite number (like 3) parameters are determined. The BGMS algorithm that they present in the paper will help confirm or falsify that.

The leading researchers involved (Weinberg Percacci Reuter...) refer to this as nonperturbative renormalizability because the theory cannot be developed by perturbing around flat space zero gravity---you have to shift over to the UV fixed point. Otherwise it behaves as you expect and does what a renormalizable theory is supposed to do.

And euh, what is this UV fix point, a ''free'' theory (which I guess it cannot be since the only free gravitational theory is given by Einstein's equations)? What does the beast look like ?? How do they control causality ? What happens to locality ? How does the coupling to matter work ? What are they doing precisely ? Are they just proposing a resummation of the perturbation series ? What do you mean by background independent (as far as I see string theory is as background independent as this approach is) ? Starting from the UV, do they get the correct theory out in the IR ? Anyway, just some simple questions.

Careful

 

[humanino]

Anyway, just some simple questions.

For so few nicely asked questions, there is a suitable simple answer : why don't you read the paper ?

 

[atyy]

The title of the thread is incorrect.

 

[Careful]

The title of the thread is incorrect.

That was my point

 

[Careful]

For so few nicely asked questions, there is a suitable simple answer : why don't you read the paper ?

Because I am sure they do not even treat 40 % of those questions, and that is just a shortlist of mine.

 

[marcus]

Here is a Steven Weinberg talk on the topic. It is basically his baby.
https://mediamatrix.tamu.edu/streams/327756/PHYS_Strings_2010_3-18-10C

If anyone tries this link and can't get the video, please let me know. My guess is that Weinberg is pleased with this paper by BGMS. We may hear something about that.

 

[marcus]

The title of the thread is incorrect.

The experts in the field certainly do call AS (nonperturbatively) renormalizable.

I forget when I first heard AS described this way, before 2007 certainly, probably by Martin Reuter. Then, if I remember, in Roberto Percacci's 2007 review article. http://arxiv.org/abs/0709.3851
After 2007 it would have been so common to refer to AS as having that property that I would not have noted individual cases. That establishes the terminology as "correct" AFAICS.

Percacci you recall organized the 2009 Perimeter conference on AS. I would say he and Steven Weinberg are the top experts. I think nothing is to be gained by flatly contradicting their usage without explanation. I think you must have meant something else, Atyy , but I can't think what?

 

[atyy]

That was my point

But we should maybe get excited that marcus likes a particle physics approach to QG, instead of Rovellian relativists are so conceptually superior :tongue:

After all, this approach falls straight out of the Wilsonian worldview, and is mentioned in the first chapter of Polchinkski.

I do understand that it is unlikely for reasons relating to black hole entropy, but all the same, Wilson alone dictates it's a formal possibility.

 

[atyy]

The experts in the field certainly do call AS (nonperturbatively) renormalizable.

I forget when I first heard AS described this way, before 2007 certainly, probably by Martin Reuter. Then, if I remember, in Roberto Percacci's 2007 review article. That establishes the terminology as "correct" AFAICS.

Percacci you recall organized the 2009 Perimeter conference on AS. I would say he and Steven Weinberg are the top experts. I think nothing is to be gained by flatly contradicting their usage without explanation. I think you must have meant something else, Atyy , but I can't think what?

But your thread title says that the paper claims that the existence of AS as a coherent theory of QG has been shown. The paper makes no such claim.

 

[Careful]

But we should maybe get excited that marcus likes a particle physics approach to QG, instead of Rovellian relativists are so conceptually superior :tongue:

After all, this approach falls straight out of the Wilsonian worldview, and is mentioned in the first chapter of Polchinkski.

I do understand that it is unlikely for reasons relating to black hole entropy, but all the same, Wilson alone dictates it's a formal possibility.

Well some 5 years ago I looked at the physics of what they are doing, not just the mathematics (because I know these people have the necessary skills to get that part right) and I don't think it is very good. There is very little room in a particle physicist's approach to move beyond ordinary expansion around Minkowski and quantizing in the radiation gauge. Of course, a simple mathematical theorem tells you that if you have a series which can be devided into two subseries one of which converges to + infinity and another to - infinity. You can perform a ressumation so that it goes to a finite number, actually, it can go to any finite number So, you lose total control of what you are doing physically: the background is not just a mathematical devise, but also tells you how to define particles, vacuum state and control causality. Hence, perturbation theory is a theory of ''small corrections to it'' in which the leading order terms have a physical significance. So, I seriously doubt it that merely changing the background is going to make the theory well defined unless you do such tricks, but those should work as well on Minkowski. I haven't looked deeply into their paper, but I haven't seen any notion like Feynman propagator or radiative Green's function; it is well known that on a curved background the former has *no* unique definition unlike in Minkowski and there are other problems associated to these constructions as well (see for example Eric Poisson's review paper about point particle motions in curved spacetime - he treats these questions in much rigor). So, you know, just computing the heat kernel is meaningless physically, such thing is uniquely defined in Euclidean signatures but not in Minkowskian ones. There, you have plenty of more choices of appropriate boundary conditions and physics tells you you have to take the right one (and as I said, there is only a unique construction in Minkowski). Anyway, these are some of my recollections of these things, it may be that I am mistaken somewhere

Careful

 

[Careful]

instead of Rovellian relativists are so conceptually superior :tongue:

On the conceptual side, all know approaches are ugly animals; apart from causal set theory I don't know any approach which even faces these issues. And Rovelli is far removed from being a deep conceptual thinker, I understood Nietzsche and Jung when I was 15, so I know what I talk about.

Careful

 

[humanino]

I understood Nietzsche and Jung when I was 15, so I know what I talk about.

It's great, I hope it was not too long ago, so maybe you will have time to tell entire communities what the final answer to high energy physics is. Until then, you may want to check your dictionary for "humility".

 

[Kevin_Axion]

Does it matter what people choose to research? String Theory, to tell the truth, isn't much better than approaches like Asymptotic Safety.

 

[tom.stoer]

@Careful: please, be careful

 

[Careful]

Does it matter what people choose to research? String Theory, to tell the truth, isn't much better than approaches like Asymptotic Safety.

The situation is very simple, so I will explain it in simple terms. Everyone is simply messing around at this moment, we need new physical input and in that respect ST scores much better than any other approach. The problem in academia is that as a young researcher you have to write research programs to get funding and you more or less have to follow those (in mathematics, it is much better, I know of professors who just keep papers in their desk and write about ''future'' ideas which are already in the pocket ). So, the general issue here, is that once you have tried your first naive shot (and we all think naive in the beginning), you just cannot say you were wrong to those people who pay you, you see. Because, then people do not take you seriously anymore while it should be exactly the opposite. This results in what I call the ''milking cow phenomenon'' where people extract as much papers as possible from something they deeply inside don't really believe in anymore. But who cares? That's the way the game works; it is precisely the reason why people get defensive about their work even if they know it is not good, because pointing it out goes against the group dynamics.

Careful

 

[humanino]

advertising your own ideas like that is very bad

The only idea I am advertising is to have the proper respect for others, and I think Weinberg put it very nicely. Although this approach is unlikely and had difficulties, nobody can tell for certain, and we must keep an open mind.

 

[humanino]

why people get defensive

The problem being that you are the one who needs to be defensive now.

 

[Careful]

The only idea I am advertising is to have the proper respect for others, and I think Weinberg put it very nicely. Although this approach is unlikely and had difficulties, nobody can tell for certain, and we must keep an open mind.

Yes, but as I pointed out, Weinberg's statement is of a *mathematical* nature. And I formally agree with the statement, but all I am saying is that you have to keep the physics under control. The simple point is - as far as I understood it in that time - that you are trying to give an alternative *definition* of the path integral. But the perturbative *definition* around Minkowksi (in the correct signature) is known to be the right way to go for other theories, so it would be very unlikely that you get the correct *phyisics* out by making such drastic moves.

Careful

 

[Careful]

The problem being that you are the one who needs to be defensive now.

Why ?

 

[tom.stoer]

... that you are trying to give an alternative *definition* of the path integral. But the perturbative *definition* around Minkowksi ... is known to be the right way to go for other theories, ...

Certainly not.

It is NOT the case that you must define the PI perturbatively. Strictly speaking it is (in most cases in QFT) not defined at all. The only chance you have seems to be a perturbative definition (using a Gaussian fixed point). But you know that this fails to catch the whole physical truth, e.g. in QCD. So you MUST go beyond perturbation theory not only in QG but in other theories as well.

 

[Kevin_Axion]

Careful, do you happen to be a string theorist? Humanino/tom.stoer do you happen to be a LQG researcher or Asymptotic Safety researcher. If the answers are no, then I'll ask, why do you care?

 

[atyy]

Yes, but as I pointed out, Weinberg's statement is of a *mathematical* nature. And I formally agree with the statement, but all I am saying is that you have to keep the physics under control. The simple point is - as far as I understood it in that time - that you are trying to give an alternative *definition* of the path integral. But the perturbative *definition* around Minkowksi (in the correct signature) is known to be the right way to go for other theories, so it would be very unlikely that you get the correct *phyisics* out by making such drastic moves.

Careful

But isn't the point that in QG, we are looking for all theories that are internally consistent. Consequently, the statement is of course mathematical in nature. Whether the physics is correct is decided by comparison with observations. The Wilson-Weinberg viewpoint is very simple, either it is consistent with a UV fixed point, like QCD, or new degrees of freedom must be introduced, like string theory. There are theories known where the fixed point is non-Gaussian, the only question is whether gravity without additional degrees of freedom is such a theory.

 

[tom.stoer]

Careful, do you happen to be a string theorist? Humanino/tom.stoer do you happen to be a LQG researcher or Asymptotic Safety researcher. If the answers are no, then I'll ask, why do you care?

Care about what?

 

[Kevin_Axion]

Why do "you" care about what Careful is saying, or any other criticism of the "hypothesis" for that matter.

 

[Careful]

It is NOT the case that you must define the PI perturbatively. Strictly speaking it is (in most cases in QFT) not defined at all. The only chance you have seems to be a perturbative definition (using a Gaussian fixed point). But you know that this fails to catch the whole physical truth, e.g. in QCD. So you MUST go beyond perturbation theory not only in QG but in other theories as well.

So then, what are your particles, what is your vacuum state, what are your physical observables ?? How do you define bound states, how do you calculate their quantum properties ?? I know what you say, but no-one has ever made sense out of these things in conventional QT. There is a big distinction by taking into account exotic classical solutions in the path integral and perturbing around those and, on the other hand, being able to define the correct observables, no ?

Careful

 

[Careful]

But isn't the point that in QG, we are looking for all theories that are internally consistent.

Well you know, not really. Such democracy of ideas has lead to the result that up till now, we don't even have a single one. We must be looking for new physical guidelines, not mathematical ones.

Consequently, the statement is of course mathematical in nature.

No, it isn't in my view.

Whether the physics is correct is decided by comparison with observations. The Wilson-Weinberg viewpoint is very simple, either it is consistent with a UV fixed point, like QCD, or new degrees of freedom must be introduced, like string theory. There are theories known where the fixed point is non-Gaussian, the only question is whether gravity without additional degrees of freedom is such a theory.

Well, the subtlety here is that we really don't know what we mean with that. It again depends on how you define the path integral; it lacks physical insight.

 

[Careful]

Careful, do you happen to be a string theorist?

No, I am in my own camp And I stopped caring about fundraising 5 years ago.

Careful

 

[atyy]

Well you know, not really. Such democracy of ideas has lead to the result that up till now, we don't even have a single one. We must be looking for new physical guidelines, not mathematical ones.

We do. String theory. In particular, AdS/CFT, which unfortuantely has already been falsified. But maybe studying it will give us some ideas. And maybe the rest of string theory will also turn out to be coherent.

 

[tom.stoer]

So then, what are your particles, what is your vacuum state, what are your physical observables ?? How do you define bound states, how do you calculate their quantum properties ?? I know what you say, but no-one has ever made sense out of these things in conventional QT. There is a big distinction by taking into account exotic classical solutions in the path integral and perturbing around those and, on the other hand, being able to define the correct observables, no ?

Ever looked at lattice gauge theories? Perhaps you do not care b/c it's conceptually boring - but they can calculate observables :-)

 

[Careful]

We do. String theory. In particular, AdS/CFT, which unfortuantely has already been falsified. But maybe studying it will give us some ideas. And maybe the rest of string theory will also turn out to be coherent.

Well as I said once, ST scores 6,5 on my personal scale and LQG 3 on 10, that is. Still, I find 6,5 to be too meager.

But some ideas of string theory are certainly worthwhile, but the strings themselves are not in my opinion. But as my stringy friends tell me, ST is moving away from this picture slowely, no ?

 

[Careful]

Ever looked at lattice gauge theories? Perhaps you do not care b/c it's conceptually boring - but they can calculate observables :-)

Yes, I know that, but as far as I know, it stops at the level of the lattice, no ? :!) I may be wrong here, I am not a specialist in this kind of approach.

 

[atyy]

Well as I said once, ST scores 6,5 on my personal scale and LQG 3 on 10, that is. Still, I find 6,5 to be too meager.

But some ideas of string theory are certainly worthwhile, but the strings themselves are not in my opinion. But as my stringy friends tell me, ST is moving away from this picture slowely, no ?

You had better be using a log scale there!

 

[Careful]

You had better be using a log scale there!

:rofl::rofl: One can never give too few points to the opponent, can one ?

 

[Careful]

It's great, I hope it was not too long ago, so maybe you will have time to tell entire communities what the final answer to high energy physics is. Until then, you may want to check your dictionary for "humility".

Ok, I apologize for having said that, although I think it is a correct statement, I should perhaps have kept my opinion for myself.

Careful