Steven Weinberg offers a way to explain inflation

[marcus]

Mtd2 spotted this paper by Steven Weinberg that just went on arxiv.
http://arxiv.org/abs/0911.3165
Asymptotically Safe Inflation
Steven Weinberg
13 pages
(Submitted on 16 Nov 2009)
"Inflation is studied in the context of asymptotically safe theories of gravitation. It is found to be possible under several circumstances to have a long period of nearly exponential expansion that eventually comes to an end."

It could be an important paper, and in any case it's kind of elegant because the inflation episode occurs naturally, by the running of constants, without having to dream up some exotic matter field.

Reuter and Bonanno already proposed something along these lines. The essential arithmetic is very simple: there is evidence of the existence of a UV fixed point for gravity where the dimensionless forms of G(k) the running Newton and Lambda(k) the running dark energy constant both converge to finite values as the length scale k -> 0

But one can see by simple dimensional reasoning that their dimensionless forms are
G(k)/k² and Lambda(k)k².

So for them to go to finite limits as k->0 we must have G(k) getting very small and Lambda(k) growing enormous.

That's just the thing to cause rapid expansion. The Newton constant is almost nothing, so nothing to hold the geometry together, and the cosmological constant---the dark energy that accelerates expansion---totally huge.

But as inflation proceeds the scale k increases, which increases G and reduces Lambda. So the process eventually (actually quite quickly) shuts itself off.

 

[marcus]

Two things about this idea seem extremely appealing.
One is the "graceful exit" from inflation. People like Andrei Linde who dream up "inflaton" inflation scenarios have a terrible problem arranging for inflation to stop.
First they have to fantasize some exotic matter field never before seen in the real world just to get inflation to begin in the first place, and then they have to go into contortions about special "slow roll" down a potential slope so that inflation will stop. It is all very ad hoc.
Weinberg (and also Reuter and Bonanno) seem to have an inflation mechanism that is the opposite of ad hoc. Everything happens naturally, has to happen, because of the running of the main constants. And you even get a "graceful exit" to inflation.

The other thing that seems so appealing is that it doesn't use any machinery that we don't have already. It is very OCCAM. Occam says not to increase the number of entities in your model (if you can avoid it.) And we already have these two entities Newton constant and Lambda. They are the two main constants that occur in Einstein's basic GR equation. Just those two and the speed of light c (if you want to count that instead of setting it to equal one.)

Weinberg spoke about this in his 6 July CERN talk, which is on video. He said he had a renewed research interest in Asymptotic Safe QG, and particularly its application to cosmology. So we have been waiting for exactly this paper to appear. And now a little over four months later, here it is.

That 6 July talk was really enlightening. Especially the last 12 minutes, which you can get to by dragging the time button to minute 58. I should get the link. Here's the video:
http://cdsweb.cern.ch/record/1188567/
and here's a link to get slides PDF if desired:
http://indico.cern.ch/conferenceDisplay.py?confId=57283

 

[Sauron]

It is curious how few attention has got a seemingly challenging paper made by such an eminent physicist.

 

[Bob_for_short]

It is curious how few attention has got a seemingly challenging paper made by such an eminent physicist.

It was made public three days ago. What do you want?

 

[hamster143]

It is curious how few attention has got a seemingly challenging paper made by such an eminent physicist.

The whole idea of an asymptotically safe QG is a big stretch. (Although, whether it's a bigger stretch than the 100+ parameter SUSY, I cannot say.)

 

[marcus]

It is curious how few attention ...

Let me review. Weinberg lectured about asym.safeQG in 1976, published about it in 1979, the year he was awarded Nobel. Then early this year he posted a paper showing renewed interest in it and (as I recall) mentioning relevance to cosmo. That was in MARCH, http://arxiv.org/abs/0903.0568
(he described "his personal view" at that point.)
THEN PERIMETER decided to have a conference on on AsymSafe QG and discussed it with
Weinberg and Weinberg said he would attend.
THEN AT CERN ON 6 July he gave a talk opening a conference, with a lot of string theorists among others, which he
1. explained his renewed interest in AS, why he thinks it is worth investigating
2. said his own research was on AS and described the application to cosmo, explaining inflation
3. said string might not be needed for unification, and might not be how the world is.
4. sketched the history of "good old quantum field theory" and suggested that periodically it plateaus and people look at alternatives and then they abandon the alternatives and QFT advances to another plateau. He sketched a rough picture of the "stock market" for QFT over time and it looked like a flight of steps, ready to take another rise.
5. mentioned the Perimeter conference on AS that he would be attending in November.

Now I would say that the whole thing went very smoothly. Most of the "news" got around quietly between March and July, and whatever shift and adjustment happened without provoking any reaction. Now we are in a different situation, different mental climate. There has been a large recent increase in attention to AsymSafe QG. Attention in the form of people doing research and attending the conference, and visibility.

The whole idea of an asymptotically safe QG is a big stretch. (Although, whether it's a bigger stretch than the 100+ parameter SUSY, I cannot say.)

Hamster, I'm curious why you see it subjectively as a "big stretch". What about it seems to you difficult to accommodate mentally?

Essentially no new concepts or mathematical entities are required, it uses the machinery already in place as of, say, 1980.
The basic issue is whether or not the renormalization flow has a UV fixed point, on a finite dimensional critical surface.
Since Reuter's 1998 paper, evidence that it has such a fixed point gradually built up until, this year, the situation reached a tipping point.

Conceptually it seems pretty simple, so I don't understand why you see it as a big mental stretch. Please explain.

 

[hamster143]

The basic issue is whether or not the renormalization flow has a UV fixed point

It's not just that. It's the question whether we live in a universe that lies on the critical surface. Since the critical surface is most likely finite-dimensional and the space of all couplings is infinite-dimensional, the a priori probability that we actually live in such universe is zero. It would require either some not-as-of-yet-understood mechanism that puts the gravity in the UV fixed point, or the incredible amount of fine-tuning, to justify this scenario.

Secondly, it's skirting the big issue: even if QFT is valid beyond Planck scale, why is it set up the way it is (SU(3)xSU(2)x1, three generations, etc.).

Fortunately, the theory is, in principle, falsifiable, if we measure enough couplings and prove that the point we get is not on the trajectory that leads to the fixed point. Unfortunately, we only know one coupling with any degree of certainty (1 in 10^5) and most of them are suppressed by powers of Plank mass, and precise measurements of those couplings are not in the cards in the foreseeable future.

 

[marcus]

It's the question whether we live in a universe that lies on the critical surface.

Sounds like you are imagining things in terms of a multiverse. AsymSafe doesn't connect with multiversy thoughts. The universe is not supposed to "lie on the critical surface".

The story here is basic 1970s Ken Wilson stuff, the renormalization group flow belonging to our one universe. There are no alternative universes or probabilities such as you seem to be imagining.

Since the critical surface is most likely finite-dimensional and the space of all couplings is infinite-dimensional, the a priori probability that we actually live in such universe is zero.

This doesn't connect with the discussion in this thread, so it does not call for a response.

 

[hamster143]

This has nothing to do with a multiverse. The question is, what happens if we take the set of coupling values in our universe and use renormalization group to take the UV limit? A priori, there's no reason to expect that we get into the fixed point, because the subspace of initial values that lead to the fixed point is measure zero in the space of all possible initial values. Contrast with QCD, where you can start with any value of coupling constant and you'll inevitably end up in the UV fixed point.

Weinberg is basically saying "look, gravity COULD be a renormalizable theory..." because, if the initial conditions are on the invariant surface, renormalization flow does not blow up near Planck mass. But it's hard to justify why it SHOULD be renormalizable, precisely because Wilson & such have disposed with the requirement.

 

[Finbar]

Hamster makes an interesting point. But the reason we know QCD flows to the fixed point is because we know the bare action and hence the underlying degrees of freedom. In the RG approach to asymptotic safety we only have average effective action and not the bare action.

If we had the bare action and then said "this is my theory of gravity and look its asymptotically safe" then we would be in the same situation as QCD.

 

[Haelfix]

Even more problematic, the critical surface could be spurious. You have to show universality, existence and stability across every type of approximation (1/epsilon expansions, truncation schemes etc) and inclusion of almost infinitely different matter terms. That is, the space of couplings most likely changes as you progressively refine your theory. No one knows how to even approach proving these things in general, so the state of the art is simply numerical investigations on various different types of simple toy models.

Even if you can show all of those things, and that's the way the world works, the problem for model builders remains the same. Eg you still lack general predictivity without actually doing the experiments that fixes the actual couplings perse (and determining whether you are or are not on the critical surface). And we are back to the problem of having to build galaxy size accelerators to pin down the dynamics of quantum gravity.

The original motivation for dropping field theory in the first place, was this generic futility argument. It didn't really matter if you found a plausible candidate theory of quantum gravity and figured out all the general principles. B/c unless you had some extra local symmetry group acting on your theory (say lots of SuSY or perhaps a conformal symmetry) you couldn't in general pin everything down uniquely. That was why string theory became so dominant, b/c there everything is fixed by consistency constraints and if you could figure out the solution, you had a unique theory across all energy scales.

Then there is the more theoretical issues (such as the wrong scaling behaviour of field theories in black holes) and so forth.

 

[hamster143]

But the reason we know QCD flows to the fixed point is because we know the bare action and hence the underlying degrees of freedom.

We don't know even that for sure. We know that a "toy QCD" with no dimension 5+ operators flows to the fixed point. There could be (there probably are) dimension 5+ operators suppressed by powers of some energy scale, and, once we reach that energy scale, QCD can do anything it wants. Below that scale the flow is in fact in the direction of a trivial UV fixed point. We tend to ignore higher-dimension operators because there's a lot of interesting dynamics even without them.

In GR, dimension 5+ operators are essential.

 

[Finbar]

unique theory? string theory? eh?

I don't follow you Haelfix?

And that black hole argument is rather silly...

 

[Haelfix]

Eh? String theory is completely unique. There are no independant adjustable free parameters. You can't 'tweak' the theory by adding new couplings or new matter content.

The black hole scaling argument is not 'silly' either! You have a major problem when general thermodynamic arguments implies degrees of freedom that scale as the area, whereas your general prediction for any *local* field theory are volume degrees of freedom.

 

[Finbar]

We don't know even that for sure. We know that a "toy QCD" with no dimension 5+ operators flows to the fixed point. There could be dimension 5+ operators suppressed by powers of some energy scale, and, once we reach that energy scale, QCD can do anything it wants. But, up to that scale, the flow is in fact in the direction of a trivial UV fixed point.

Indeed, QCD should be viewed as an effective theory and so should asymptotically safe gravity(if it exists) otherwise we won't get unification. The point with asymptotic safety is that we don't need to go beyond QFT or the symmetries we are aware of in nature to quantise gravity. Its just a call to Occam's razor.

 

[Finbar]

Eh? String theory is completely unique. There are no independant adjustable free parameters. You can't 'tweak' the theory by adding new couplings or new matter content.

The black hole scaling argument is not 'silly' either! You have a major problem when general thermodynamic arguments implies degrees of freedom that scale as the area, whereas your general prediction for any field theory are volume degrees of freedom.

So your telling me there is only one string theory, one vacuum? I'm not so sure.


It is a silly argument. The argument is that all QFT should be conformal at there UV fixed point. But an event horizon is not at the fixed point. Clearly an event horizon is an IR property as I can have an arbitrarily large black hole. If I could have a black hole with a radius of well under the Planck length then it would be a problem. But asymptotic safety predicts that black holes cannot have a mass of less than the Planck mass. So at the UV fixed point there is no horizon and hence no contradiction.

 

[Haelfix]

I can't decipher your last post. A few remarks.

1) There are many QFTs, an infinite space of possible theories. Now, each particular QFT typically has a single vacuum (or possibly multiple meta stable vacuums). String theory is the opposite. There is one single theory, but it has a large, possibly infinite amount of classical solutions. This isn't just pedantic, its a big difference. So for instance you can never talk about the critical surface of coupling constants in string theory, b/c that surface is a universal point.

2) "An event horizon is not at the fixed point", "At the UV fixed point there is no horizon", "But asymptotic safety predicts that black holes cannot have a mass of less than the Planck mass"

Those sentences don't make much sense... Nor do they have anything to do with the scaling properties of field theories.

 

[Finbar]

I can't decipher your last post. A few remarks.

1) There are many QFTs, an infinite space of possible theories. Now, each particular QFT typically has a single vacuum (or possibly multiple meta stable vacuums). String theory is the opposite. There is one single theory, but it has a large, possibly infinite amount of classical solutions. This isn't just pedantic, its a big difference. So for instance you can never talk about the critical surface of coupling constants in string theory, b/c that surface is a universal point.

2) "An event horizon is not at the fixed point", "At the UV fixed point there is no horizon", "But asymptotic safety predicts that black holes cannot have a mass of less than the Planck mass"

Those sentences don't make much sense... Nor do they have anything to do with the scaling properties of field theories.

1) There is at least 5 string theories which are conjectured to be all low energy approximations to M-theory.

2) Why doesn't it make sense? The UV fixed point is where the energy scale goes to infinity or the length scale goes to zero. Classical general relativity where one finds event horizons is the IR approximation to the theory.

Think of it this way if we ignore quantum effects we get black holes in classical relativity. Hence they are a feature of the theory at energies much lower than the Planck scale. The classical theory however will break down as the curvature diverges at the central singularity, but certainly not at the event horizon of a macroscopic black hole. The fact that the curvature diverges at the singularity implies that we need to use a quantum theory. So its here that we need to worry about the scaling of he theory not at the horizon.

To make sure, are you talking about the arguments in this paper?

http://arxiv.org/pdf/0709.3555

If not and you have some other argument can you show me another paper?

 

[atyy]

"... the asymptotic safety scenario. The recourse to uncontrolled truncations of the effective action, however, makes this program difficult to justify from a mathematical physics perspective." http://arxiv.org/abs/0906.5477

 

[MTd2]

1) There is at least 5 string theories which are conjectured to be all low energy approximations to M-theory.

All 5 superstring theories are the same, it`s just that they are different point of views of the same thing. As for M-Theory, I am not sure if there is just 1 coupling constant, given that thre are 3 fundamental entities, M2-branes, M5 branes and D0 branes.

Having said that, I really don`t like the fact that superstrings are both unique and have a huge number o classical low energy solutions. Sounds like what adjusting strings like epicycles until it fits a model.

 

[atyy]

All 5 superstring theories are the same, it`s just that they are different point of views of the same thing. As for M-Theory, I am not sure if there is just 1 coupling constant, given that thre are 3 fundamental entities, M2-branes, M5 branes and D0 branes.

Having said that, I really don`t like the fact that superstrings are both unique and have a huge number o classical low energy solutions. Sounds like what adjusting strings like epicycles until it fits a model.

Since there are only a finite number of possible low energy solutions, maybe none of them will fit this universe - so it isn't like epicycles.

 

[humanino]

Since there are only a finite number of possible low energy solutions, maybe none of them will fit this universe - so it isn't like epicycles.

Finite, like how many ? If there one solution per fermion in the visible universe ? Is there one per wavelength accomplished since the big bang by all photons in the visible universe ? Can you compare your number of solutions to anything "reasonably definable" ?

 

[atyy]

Finite, like how many ? If there one solution per fermion in the visible universe ? Is there one per wavelength accomplished since the big bang by all photons in the visible universe ? Can you compare your number of solutions to anything "reasonably definable" ?

10^500 or whatever the latest number is.

 

[humanino]

10^500 or whatever the latest number is.

I understand that this is a lower bound, and that the uncertainty is in the exponent, and it would not be a surprise if this exponent would grow by an order of magnitude. Besides, I asked you to name anything reasonable counting that many.

 

[atyy]

Besides, I asked you to name anything reasonable counting that many.

Oh, I don't know - why does that matter?

 

[humanino]

Oh, I don't know - why does that matter?

In principle, it does not, at least to me. But in practice, I do not think it is fair to say "there is a finite number of vacua, so the theory is falsifiable" because we need to somehow reduce the number of possible vacua, we could possibly not test all those predictions even in principle.

 

[atyy]

In principle, it does not, at least to me. But in practice, I do not think it is fair to say "there is a finite number of vacua, so the theory is falsifiable" because we need to somehow reduce the number of possible vacua, we could possibly not test all those predictions even in principle.

I agree - but won't it keep experimentalists happy for longer?

Well, a bit more seriously, what do you think of these guys comments following "could we imagine showing that the data is fit by none of these theories, thus falsifying the theory?" on p37 of http://arxiv.org/abs/hep-th/0701050

 

[Haelfix]

"1) There is at least 5 string theories which are conjectured to be all low energy approximations to M-theory."

They are all dual to each other, and hence one theory with one hilbert space (called M theory -- not to be confused with the M theory that is a limit of 11 dimensional SUGRA)

"Classical general relativity where one finds event horizons is the IR approximation to the theory."

The ultra high energy behaviour of quantum gravity is and must be GR again. It becomes classical again at ultra high energy scales, where particle collisions and the (trans) Planckian energy densities simply creates larger and larger black holes (this is called asymptotic darkness). It is this limit that is problematic for a field theory description of gravity, not the IR limit.

So the argument is this: The high energy limit for any consistent field theory (eg not effective), must be asymptotically free or asymptotically safe, and hence scale invariant. The problem (as that paper you linked explains) is you cannot simultaneously be scale invariant, and still describe the classical theory of Einstein gravity (that would be Weyl gravity). So there is a clash.

 

[atyy]

So the argument is this: The high energy limit for any consistent field theory (eg not effective), must be asymptotically free or asymptotically safe, and hence scale invariant. The problem (as that paper you linked explains) is you cannot simultaneously be scale invariant, and still describe the classical theory of Einstein gravity (that would be Weyl gravity). So there is a clash.

How about this comment by Distler? "In any case, the existence of a “quantum” conformal symmetry in quantum gravity is compatible with there being a nontrivial dimensionful scale in the theory, so I don’t see a-priori why it’s incompatible with black holes." http://golem.ph.utexas.edu/~distler/blog/archives/001585.html

 

[humanino]

So the argument is this: The high energy limit for any consistent field theory (eg not effective), must be asymptotically free or asymptotically safe, and hence scale invariant. The problem (as that paper you linked explains) is you cannot simultaneously be scale invariant, and still describe the classical theory of Einstein gravity (that would be Weyl gravity). So there is a clash.

IIRC, in this approach the UV limit is ultralocal and 2D.

 

[Haelfix]

I don't know what he has in mind exactly there, but somehow the field theory has to lose a dimension (not 2 but 1) for the scaling to match. How that is realized, is something that people will need to explain. I'm not saying its impossible, but something peculiar needs to take place. (I am aware of the talk about losing dimensionality, but that's more at the level of the space of coupling constants)

He's very correct that all bets are off in DeSitter space. No one knows or even has an expectation of what the high energy behaviour is like there. There is no SMatrix!

 

[MTd2]

No one knows for sure how many low energy solutions there are in 10^500. Could be infinite , could be finite but very big, there are many ways to count, each one with different plausible consistency conditions. Heh, but isn`t this offtopic?

 

[atyy]

No one knows for sure how many low energy solutions there are in 10^500. Could be infinite , could be finite but very big, there are many ways to count, each one with different plausible consistency conditions. Heh, but isn`t this offtopic?

I guess the corresponding question in Asymptotic Safety is how many scenarios are there? Do predictions change depending on matter content? Or are there "universal" predictions, eg. spectral dimension (though that alone may not nail down AS, since it is consistent with Horava, if the scalar mode can be fixed). Also, can the spectral dimension be measured - in CDT one of these "dimension" measures was defined with a particle diffusing on a fixed background - isn't this at odds with background independence - so can it be measured with realistic matter content?

 

[MTd2]

There is really no similar situation in asymptotic safety. Asymptotic safety is phase state of certain theories in which all coupling constant are constrained to a finite value. This value is a vector that can span finite dimensional surface, formed by coupling constants which cannot be restrained while transitioning to a low energy scale, like the others are.

 

[atyy]

There is really no similar situation in asymptotic safety. Asymptotic safety is phase state of certain theories in which all coupling constant are constrained to a finite value. This value is a vector that can span finite dimensional surface, formed by coupling constants which cannot be restrained while transitioning to a low energy scale, like the others are.

But they'll need matter to make predictions. I do agree whether pure gravity is safe is an interesting question, but from there to incorporating matter what happens?

 

[MTd2]

Hmmm. Guess what the topic of this thread is about! :) The article should be the answer for your question.

 

[atyy]

(I am aware of the talk about losing dimensionality, but that's more at the level of the space of coupling constants)

I think there are two sorts of losing dimensionality. The first is in the space of coupling constants where the critical surface is finite dimensional (latest number is 3, I think, in Codello's papers). The second is the "anomalous dimension" which is supposed to be 2, I think this is what humanino was thinking about. There's also a "spectral dimension" which seems to be thought of as related to the anomalous dimension, but I'm not sure if that's rigourous - anyway that is supposed to be ~2.

 

[atyy]

Hmmm. Guess what the topic of this thread is about! :) The article should be the answer for your question.

Does Weinberg mention Percacci's GraviGUT?

 

[MTd2]

No, he just lays out a way to do the calculation, in generic terms.

 

[atyy]

No, he just lays out a way to do the calculation, in generic terms.

BTW, did you notice Lubos's comment "Now, you may say that physicists know 5 or 12 or 2009 alternatives to string/M-theory - except that 4 or 11 or 2008 of them already reside at the dumping ground of physics. (http://motls.blogspot.com/2009/10/nature-nyt-report-demise-of-lorentz.html)". This means he thinks that there's currently one reasonable approach other than strings - I'm guessing that's Asymptotic Safety?

 

[Finbar]

"1) There is at least 5 string theories which are conjectured to be all low energy approximations to M-theory."

They are all dual to each other, and hence one theory with one hilbert space (called M theory -- not to be confused with the M theory that is a limit of 11 dimensional SUGRA)

"Classical general relativity where one finds event horizons is the IR approximation to the theory."

The ultra high energy behaviour of quantum gravity is and must be GR again. It becomes classical again at ultra high energy scales, where particle collisions and the (trans) Planckian energy densities simply creates larger and larger black holes (this is called asymptotic darkness). It is this limit that is problematic for a field theory description of gravity, not the IR limit.

So the argument is this: The high energy limit for any consistent field theory (eg not effective), must be asymptotically free or asymptotically safe, and hence scale invariant. The problem (as that paper you linked explains) is you cannot simultaneously be scale invariant, and still describe the classical theory of Einstein gravity (that would be Weyl gravity). So there is a clash.

Your argument just makes no sense its just plainly illogical. If the theory is Asymptotically safe then its not the classical(Einstein Hilbert) theory at the UV fixed point its the conformal theory so there are no black holes. You say "The ultra high energy behavior must be GR again" why? I'm sorry but that's nonsense. In the paper I cited they make no such claim either.

Basically the argument is made by people who don't understand the Wilson. They think that what holds in the IR holds in the UV.

 

[MTd2]

BTW, did you notice Lubos's comment "Now, you may say that physicists know 5 or 12 or 2009 alternatives to string/M-theory - except that 4 or 11 or 2008 of them already reside at the dumping ground of physics.

Only you should only trust him when only he is talking about string, only.

 

[Haelfix]

Your argument just makes no sense its just plainly illogical. If the theory is Asymptotically safe then its not the classical(Einstein Hilbert) theory at the UV fixed point its the conformal theory so there are no black holes. You say "The ultra high energy behavior must be GR again" why? I'm sorry but that's nonsense. In the paper I cited they make no such claim either.

Basically the argument is made by people who don't understand the Wilson. They think that what holds in the IR holds in the UV.

Yea, you seem to miss the point of that paper, b/c that's exactly what it does say. The author is one of Tom Bank's coauthors (whom he thanks at the end of the manuscript), and the original idea goes back to this paper:
hep-th/9812237. Also hep-th/9906038; gr-qc/0201034.

Tom is probably one of three or four people in the world with the best understanding of critical points in high energy physics...

 

[marcus]

But they'll need matter to make predictions. I do agree whether pure gravity is safe is an interesting question, but from there to incorporating matter what happens?

Does Weinberg mention Percacci's GraviGUT?

In line with these questions raised earlier, including matter is evidently critical and we could try to see what the relation is between Weinberg's paper and the recent ones of Percacci.
As far as I know, Percacci (who was the main organizer of the recent AsymSafe conference at Perimeter) is the one who has done the most towards including matter in the asymptotic safety picture. It might help to have the abstracts of his recent papers handy.

As a reminder, so we can carry over some of the understanding gained in the other thread, here is the initial post of the GraviGUT thread:

http://arxiv.org/abs/0910.5167
Gravity from a Particle Physicist's perspective
R. Percacci
Lectures given at the Fifth International School on Field Theory and Gravitation, Cuiaba, Brazil April 20-24 2009. To appear in Proceedings of Science
(Submitted on 27 Oct 2009)
"In these lectures I review the status of gravity from the point of view of the gauge principle and renormalization, the main tools in the toolbox of theoretical particle physics. In the first lecture I start from the old question "in what sense is gravity a gauge theory?" I will reformulate the theory of gravity in a general kinematical setting which highlights the presence of two Goldstone boson-like fields, and the occurrence of a gravitational Higgs phenomenon. The fact that in General Relativity the connection is a derived quantity appears to be a low energy consequence of this Higgs phenomenon. From here it is simple to see how to embed the group of local frame transformations and a Yang Mills group into a larger unifying group, and how the distinction between these groups, and the corresponding interactions, derives from the VEV of an order parameter. I will describe in some detail the fermionic sector of a realistic "GraviGUT" with SO(3,1)\times SO(10) \subset SO(3,11). In the second lecture I will discuss the possibility that the renormalization group flow of gravity has a fixed point with a finite number of attractive directions. This would make the theory well behaved in the ultraviolet, and predictive, in spite of being perturbatively nonrenormalizable. There is by now a significant amount of evidence that this may be the case. There are thus reasons to believe that quantum field theory may eventually prove sufficient to explain the mysteries of gravity."

Garrett's (slightly cryptic) comment was:

Hello PF folk.

If you believe the Dirac equation in curved spacetime, and you believe Spin(10) grand unification, then a Spin(3,11) GraviGUT, acting on one generation of fermions as a 64 spinor, seems... inevitable.

Also, it's pretty.

And it's up to you whether or not to take seriously or not the observation that this whole structure fits in E8. Personally, I take it seriously. Slides are up for a talk I gave at Yale:

http://www.liegroups.org/zuckerman/slides.htmlGarrett

 

[marcus]

More material in line with the questions Atyy raised:

But they'll need matter to make predictions. I do agree whether pure gravity is safe is an interesting question, but from there to incorporating matter what happens?

Does Weinberg mention Percacci's GraviGUT?

I just got the link to Percacci's October 2009 GraviGUT paper. There was a follow-up November paper.

http://arxiv.org/abs/0911.0386
Renormalization Group Flow in Scalar-Tensor Theories. I
Gaurav Narain, Roberto Percacci
18 pages, 10 figures
(Submitted on 2 Nov 2009)

==quote from the conclusions==

Another direction for research is the inclusion of other matter fields. As discussed in the introduction, if asymptotic safety is indeed the answer to the UV issues of quantum field theory, then it will not be enough to establish asymptotic safety of gravity: one will have to establish asymptotic safety for a theory including gravity as well as all the fields that occur in the standard model, and perhaps even other ones that have not yet been discovered. Ideally one would like to have a unified theory of all interactions including gravity, perhaps a GraviGUT along the lines of [45]. More humbly one could start by studying the effect of gravity on the interactions of the standard model or GUTs.

Fortunately, for some important parts of the standard model it is already known that an UV Gaussian FP exists, so the question is whether the coupling to gravity, or some other mechanism, can cure the bad behavior of QED and of the Higgs sector. That this might happen had been speculated long ago [33]; see also [46] for some detailed calculations.

It seems that the existence of a GMFP for all matter interactions would be the simplest solution to this issue. In this picture of asymptotic safety, gravity would be the only effective interaction at sufficiently high scale. The possibility of asymptotic safety in a nonlinearly realized scalar sector has been discussed in [47]. Aside from scalar tensor theories, the effect of gravity has been studied in [48] for gauge couplings and [49] for Yukawa couplings.
==endquote==

The abstract goes right to the cosmology issue, which is likely to be important in establishing (or refuting) asymsafe QG+matter.

==quote from abstract==
We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self consistent, in the sense that when the scalar self couplings are switched off, their beta functions also vanish. Complete, explicit beta functions that could be applied to a variety of cosmological models are given in a five parameter truncation of the theory in d=4. In any dimension d>2 we find that the flow has only a "Gaussian Matter" fixed point, where all scalar self interactions vanish but Newton's constant and the cosmological constant are nontrivial... These findings are in accordance with the hypothesis that these theories are asymptotically safe.
==endquote==

 

[Chronos]

I'm just curious where Weinberg is going with this. It appears he has something in mind, be it string, QFD or whatever. String, which cannot be wrong, appears to have limited utility as a predictive tool. On the other hand, renormalization, which cannot be right, has great utility as a predictive tool.

 

[atyy]

I'm just curious where Weinberg is going with this. It appears he has something in mind, be it string, QFD or whatever. String, which cannot be wrong, appears to have limited utility as a predictive tool. On the other hand, renormalization, which cannot be right, has great utility as a predictive tool.

In fact renormalization is key. Renormalization says that our current theories are only low energy effective theories, and gives us two broad classes of options for the high energy theory. The first class is that the high energy theory contains the same symmetries and degrees of freedom as the low energy theory - this is asymptotic safety. The second class is that the high energy theory contains very different symmetries and degrees of freedom - this is called unification in high energy physics, or emergence in condensed matter physics, where for example, phonons are degrees of freedom at low energy that emerge from vastly different degrees of freedom at high energy. The second class of theories is presumably vaster (though it seems string theory is the only known member of this class so far), since many different high energy theories could flow to the same low energy theory, which is why they say the renormalization group is a semigroup. However, in the first class, the renormalization group can in principle be reversed since the degrees of freedom are the same, and this is the Asymptotic Safety scenario - or scenarios, since there may be more than one way to include matter.

 

[Finbar]

Yea, you seem to miss the point of that paper, b/c that's exactly what it does say. The author is one of Tom Bank's coauthors (whom he thanks at the end of the manuscript), and the original idea goes back to this paper:
hep-th/9812237. Also hep-th/9906038; gr-qc/0201034.

Tom is probably one of three or four people in the world with the best understanding of critical points in high energy physics...

The paper does't say anywhere that the action in the UV will be Einstein-Hilbert. We know its Einstein-Hilbert in the IR but it certainly not in the UV. Their argument is based on the IR scaling being different from the UV. But this is fine because the scaling will change as we flow from the IR to the UV. In the conclusion they say

"We believe this counter-argument does not hold because the asymptotic safety scenario is based on the assumption that gravity is a valid low energy approximation to some putative local quantum field theory. Therefore at least in its regime of validity it should be trusted. In particular it should be trusted to describe the horizons of large black holes, since as can be seen from Eq. 31 the more massive a black hole is, the lower is the curvature at the horizon."

But if the curvature is low then we are still in the Einstein Hilbert low energy regime so I don't expect the scaling to be conformal. Its only when the curvature is high that we approach the fixed point and the scaling should be conformal. Thus we approach the high energy regime only for a Planck sized black hole.

Either their black hole argument is correct and gravity cannot be described as a QFT or there is a logical inconsistency in their argument in there argument and gravity can be described by a QFT. I've pointed out the logical inconsistency and I think its pain to see if you look a little beyond the surface of their papers.

In the end though I think their papers are good because they really give a physical meaning to Asymptotically safe gravity. That is any asymptotically safe theory of gravity should not contain black holes in the Planck regime.

 

[marcus]

I'm just curious where Weinberg is going with this. ... renormalization, which cannot be right, has great utility as a predictive tool.

In fact renormalization is key. Renormalization says that our current theories are only low energy effective theories, and gives us two broad classes of options for the high energy theory. The first class is that the high energy theory contains the same symmetries and degrees of freedom as the low energy theory - this is asymptotic safety. The second class is that the high energy theory contains very different symmetries and degrees of freedom - this is called unification in high energy physics, or emergence in condensed matter physics, where for example, phonons are degrees of freedom at low energy that emerge from vastly different degrees of freedom at high energy. The second class of theories is presumably vaster (though it seems string theory is the only known member of this class so far), since many different high energy theories could flow to the same low energy theory, which is why they say the renormalization group is a semigroup. However, in the first class, the renormalization group can in principle be reversed since the degrees of freedom are the same, and this is the Asymptotic Safety scenario - or scenarios, since there may be more than one way to include matter.

Good question and what I think is a valuable concise answer---one I want to carry along because this exchange seems essential to the thread.
Chronos to get more of an idea where S.W. is going, what he has in mind, you could watch his 6 July video. It presents an overarching vision of where things are going in high energy physics. The pendulum swinging back to field theory and the 1970s Wilsonian renormalization approach. Scale dependence of the constants you plug into the theory is really "how the world is". He says "I don't want to discourage anyone from working in string theory, but it might turn out that string theory is not needed. It might not be how the world is."

That talk seems to have upset a lot of people. It was the opening talk of a CERN conference on the state and prospects of high energy physics, with a large audience including a lot of string theorists. The paper that later came out from that talk was considerably toned down and left out good stuff where he gave an overview of the growth of quantum field theory since the 1920s. One of his slides sketched cyclic waves of theoretician's fashion that have resulted in a kind of staircase rise. Field theory as he depicted it, has periods of rapid advance that encounter problems which then lead to a temporary lull during which radical alternatives are tried and don't work out. Then after that plateau period, field theory has (historically at least) had another surge and has risen to the next plateau.

He wasn't claiming to know the future--the tone was very modest. In effect saying " This is just how I see it. This is why I'm working on asymptotic safe (with the cosmology application) now."
Well you asked what does he have in mind. You asked where is he going with this. That talk is the most explicit answer I know. It presents an overarching vision of the past 80 years or so of high energy physics and where he thinks its going and how renormalization fixed points fit into that.

One thing that impressed me is how gentle and unarrogant. He is skillful at speaking carefully, with correctly qualified statements, without seeming pedantic. Nice low-pressure personality. The first 57 minutes are a historical overview--then he starts discussing his current research interest and explaining why this particular track.

 

[marcus]

About the idea that "renormalization cannot be right"----which I think was part of a tongue-in-cheek witticism---that raises the interesting question of why the world seems to work that way. The Perimeter Asymptotic Safety conference had several papers offering mechanisms to explain the flow of parameters with scale.

Atyy gave a concise account. In much of field theory you keep the same formula, you just gradually change the parameters you plug into it.

The "form of the Lagrangian" remains the same, but its coupling constants "run" as the relevant energy ramps up, or as you zoom the microscope in.

And the basic formula of the theory can have symmetries at high energy which disappear as the energy declines. That is, there can be terms in the basic formula which are negligible at one scale (and therefore do not disturb the symmetry) but which become large and significant at another scale.

Well this can be so unintuitive to you that your reaction is it must be all bunk and hokum.
But give Steven Weinberg a break! He is a nice guy and experienced and wise. And a lot of people find the running of constants with scale to be actually intuitive! It makes sense to them that nature should behave that way! We have to be tolerant of each other. We have different attitudes about certain things.

Personally I like running constants a lot. And also what is called "shielding and antishielding". How forces can change depending on the vacuum in between. The role that the vacuum plays. And I have glimmerings of intuition about how running constants could arise in nature. Interesting mechanisms explaining it have been offered. My attitude is that the renormalization group flow, that modifies constants with scale, is actually not hokum, or a dishonorable kludge (which you might think) but is elegant, and economical. The idea that you can make do with a single formula (if it is the right one) just by letting the constants run.

Anyway, have another look at Atyy's brief summary and see if you can look at things more from Weinberg's perspective. And remember his CERN talk caused a lot of nervous upset denial and clamor, which is real nice to hear and enjoyable to listen to.
If you want the video it is here:
http://cdsweb.cern.ch/record/1188567/