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MTd2
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Hmmm. Guess what the topic of this thread is about! :) The article should be the answer for your question.
Haelfix said:(I am aware of the talk about losing dimensionality, but that's more at the level of the space of coupling constants)
MTd2 said:Hmmm. Guess what the topic of this thread is about! :) The article should be the answer for your question.
MTd2 said:No, he just lays out a way to do the calculation, in generic terms.
Haelfix said:"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 said: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.
Finbar said: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.
atyy said: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?
atyy said:Does Weinberg mention Percacci's GraviGUT?
marcus said: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 [tex]SO(3,1)\times SO(10) \subset SO(3,11)[/tex]. 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 said: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
atyy said: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?
atyy said:Does Weinberg mention Percacci's GraviGUT?
Chronos said: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.
Haelfix said: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...
Chronos said:I'm just curious where Weinberg is going with this. ... renormalization, which cannot be right, has great utility as a predictive tool.
atyy said: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.
marcus said: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.
Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.marcus said: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.
friend said:Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.
If the "constants" change, then does this just make them another kind of field in QFT? Or are the parameters that change the "constants" not the same as the spacetime coordinates of QFT? You did mention scale which depends on spacetime coordinates.
friend said:Aren't mass and charge also compling constants. Do you mean that these can change with scale? I don't know any reason why they shouldn't change.
If the "constants" change, then does this just make them another kind of field in QFT? Or are the parameters that change the "constants" not the same as the spacetime coordinates of QFT? You did mention scale which depends on spacetime coordinates.
marcus said:None of this variation depends on spacetime coordinates, it does not vary with position. It varies only with the degree of coarseness or refinement with which one is viewing the process.
friend said:The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?
friend said:The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?
atyy said:Yes. Take a look at Eq (A.1) and (A.2) of http://relativity.livingreviews.org/Articles/lrr-2006-5/ . The LHS of (A.1) is taken over everything less than Lambda, while the RHS is taken over everything less than (Lamda-dl), because you coarse grained over dl as defined in (A.2).
friend said:So you're saying the constants change because of coarse graining the integration variable? Or is there more to it than that? Thanks.
And a coarser grain means you're looking at a smaller scale?atyy said:That's all. Very simple conceptually, but very demanding technically.
friend said:And a coarser grain means you're looking at a smaller scale?
friend said:Is this more demanding because they're trying to solve this coarse graining analytically instead of numerically on a computer?
friend said:The only way I can (presently) imagine this is if, say, the interval of integration in the path integral changes from minus to plus infinity to something smaller. Then I can understand how the coupling constants would change. Is this what's going on?
marcus said:That sounds a deal more sensible, and satisfactory to friend, than what I had to say. I'd erase my posts that struggle with the idea of renormalization group flow, except I still find it mysterious.
And I don't. I call them "ran constants" because they feel so. They want to be just constants but many theorists make them run to make ends meet. Although it is a crying rubbish, some theorists show themselves off as cool.marcus said:Personally I like running constants a lot.
Haelfix said:Losing a dimension of space is a highly destructive operation to have take place. All the degrees of freedom of the extra dimension must conspire to cancel somehow (nonlocally), and so forth.
Haelfix said:"The paper does't say anywhere that the action in the UV will be Einstein-Hilbert."
Umm, from the abstract
"The argument is based on black-hole domination of the high energy spectrum of gravity "
Later
"However, our experience with gravity has shown that once enough energy is concentrated
in a given region a black hole will form. As far as our understanding goes, the high energy spectrum of GR is dominated by black holes. More technically, it is expected that in theories of gravity, black holes will provide the dominant contribution to the large energy
asymptotics of the density of states as a function of the energy. "
And they go on to write down a classical Schwarzschild solution for their high energy scaling behaviour. Thats EH gravity...
Anyway, trivially all of this was known long before this paper reviewed it. Asymptotic darkness has a tension with universal field theories (whether free or safe). Something has to give. The AD scenario is pretty airtight from an SMatrix and thermodynamic point of view (even string theorists concede that it replaces their theory at transplanckian energies), the question is how do you smoothly interpolate between the regimes. Losing a dimension of space is a highly destructive operation to have take place. All the degrees of freedom of the extra dimension must conspire to cancel somehow (nonlocally), and so forth.