LHC, supersymmetry and strings

[eendavid]

I am not familiar with beyond-gravity results (as far as I can tell, the drawback is that one has to put matter in by hand), so I'd only like to comment on different ambitions for quantum gravity. String theory (also string field theory) needs a background (not necessary Minkowski), and as such can not be used to study dynamics in quantum gravity. This is not only a mathematical drawback; I think the limitations for studying the physics are often overlooked. So, only looking at gravity, the loop program is much more ambitious.

 

[josh1]

No. But have you ever heard of anyone saying that there is a PROOF that the single unifying M-theory exists?

Yes! Originally there where five known string theories. What witten showed was that the these five theories together with an additional eleven-dimensional theory where in fact all related by a set of dualities in a way that clearly shows that rather than being separate theories, they where actually just solutions of a unique underlying theory. More generally, these solutions are actually just corners of a larger space of solutions parametrized by massless Lorentz scalars called moduli and that the unique theory underlying the six known corners of moduli space actually underlies all of moduli space as well as solutions unrelated to the others by the continuous variation of moduli. Discovering what the principles of this unique theory are is the goal that drives all of string theory research. That there is such an underlying theory shouldn’t be too much of a shock to anyone who knows that there are no freely adjustable parameters whatsoever in string theory. In particular, the couplings of all the known interactions are not inserted as constants as they are in conventional particle physics based on QFT (or the immirzi-parameter in LQG), but are rather controlled dynamically in string theory by the vacuum expectation value of one of the moduli called the dilaton.

Having said this however, I think you might be very interested to know that there is one very esteemed string theory researcher named Tom Banks who believes that it is incorrect to view different points in moduli space as solutions of the same unique theory. His argument is based on the idea that theories should ultimately be distinguished from each other in terms of their fundamental degrees of freedom, which experience working in terms of QFT and the renormalization group suggests are always to be found at UV fixed points. He then argues that different solutions will in general have different UV fixed points and so should be regarded as different theories. But even so, these different “theories” are still related to each other as I’ve explained. He is the only one I know of that has argued for this point of view and it has in any event never been particularly influential.

 

[Demystifier]

String theory (also string field theory) needs a background (not necessary Minkowski), and as such can not be used to study dynamics in quantum gravity.

Not necessarily. Perhaps gravity at the fundamental level really is not geometry, but a spin-2 field on a Minkowski spacetime. The Einstein equation, of course, suggests a different picture, but maybe the Einstein equation is just an approximation.

 

[Demystifier]

Yes! Originally there where five known string theories. What witten showed was that the these five theories together with an additional eleven-dimensional theory where in fact all related by a set of dualities in a way that clearly shows that rather than being separate theories, they where actually just solutions of a unique underlying theory. More generally, these solutions are actually just corners of a larger space of solutions parametrized by massless Lorentz scalars called moduli and that the unique theory underlying the six known corners of moduli space actually underlies all of moduli space as well as solutions unrelated to the others by the continuous variation of moduli. Discovering what the principles of this unique theory are is the goal that drives all of string theory research. That there is such an underlying theory shouldn’t be too much of a shock to anyone who knows that there are no freely adjustable parameters whatsoever in string theory. In particular, the couplings of all the known interactions are not inserted as constants as they are in conventional particle physics based on QFT (or the immirzi-parameter in LQG), but are rather controlled dynamically in string theory by the vacuum expectation value of one of the moduli called the dilaton.

If you take a new textbook or review of string theory, you will still find the derivation of 5 different string theories. You will not find a derivation of these 5 theories from a single unified theory. Yes, you will find the derivation of the dualities between them. But some of these dualities are present only on some specific topological backgrounds or only in some specific limits of the coupling constants.

Roughly speaking, the fact that
f(x)=x
and
g(x)=x+x^2
are the same for small x does prove that f(x) and g(x) are different corners of the same theory.
(For example, such a theory could be
M(x)=x+cx^2
where c is arbitrary.)

Of course, in string theory the relations are much more stringent than in the simple toy model above, which is very suggestive. Still, there is no proof that the unifying M-theory exists. If you disagree, show me the paper that claims the opposite!

 

[Demystifier]

That there is such an underlying theory shouldn’t be too much of a shock to anyone who knows that there are no freely adjustable parameters whatsoever in string theory.

But it is a shock. If I formulate, e.g., a heterotic E8XE8 string theory for a small coupling constant, one naively expects that a large coupling constant limit of it will still be a heterotic E8XE8 string theory, not some other string theory.

 

[Demystifier]

Josh1, as a counter example see also my
http://xxx.lanl.gov/abs/hep-th/0605250
which demonstrates that string theories that are T-dual to each other may not be equivalent at a more fundamental level. The point is that dualities show that SOME physical properties of dual theories are the same, but not ALL properties. In the case of T-duality, the shape of the string is also considered physical, which is certainly not the same for the T-dual strings.

 

[josh1]

Josh1, as a counter example see also my
http://xxx.lanl.gov/abs/hep-th/0605250
which demonstrates that string theories that are T-dual to each other may not be equivalent at a more fundamental level. The point is that dualities show that SOME physical properties of dual theories are the same, but not ALL properties. In the case of T-duality, the shape of the string is also considered physical, which is certainly not the same for the T-dual strings.

I didn't mean to say that the properties of the theories are all the same, but just that they are all "formally" related by various dualities etc. The challenge is to understand why these different theories should be related in these very precise ways nonetheless. If all the theories represented by points in moduli space where the same physically, there would be no problem. So this whole thing is very mysterious in that we have a collection of theories which naively should have no right to be related to each other in such precise ways but apparently are. This was the shock witten gave the physics community in the early nineties and kicked off the so-called "second string revolution".

 

[Demystifier]

I didn't mean to say that the properties of the theories are all the same, but just that they are all "formally" related by various dualities etc. The challenge is to understand why these different theories should be related in these very precise ways nonetheless. If all the theories represented by points in moduli space where the same physically, there would be no problem. So this whole thing is very mysterious in that we have a collection of theories which naively should have no right to be related to each other in such precise ways but apparently are. This was the shock witten gave the physics community in the early nineties and kicked off the so-called "second string revolution".

With such a softened claim I fully agree.

 

[marcus]

Marcus, thank you for pointing out to me that the loop program is wider than I thought.
Is there a kind of a review (not too technical if possible) of various such beyond-gravity achievements of the loop approach?

Hi Demy, we were talking about GOALS, weren't we? As I recall you indicated a preference for the string framework or philosophy which depended on your perception of it as more AMBITIOUS.

.. the string program is much more ambitious than the loop program.

If the ONLY goal of the string approach was to have a consistent quantum gravity, then I would certainly prefer loops over strings...

That is a really interesting issue. I want to get back to that and be more clear about it. I think that some of the approaches being worked on in the loop community are arguably more ambitious because they seek to find the fundamental degrees of freedom describing matter, and geometry as well.

I don't know anywhere in string writing where there is such a big goal, perhaps you can point me to something on the web----I mean a formalism aimed at being able to write down the quantum state of the universe--quantum state of global space or spacetime geometry (and matter).

As far as I know stringy formalism does not have a dynamical quantum state of geometry---except in a localized perturbative sense e.g. gravitons on a fixed background---or in a rather contrived setting with negative cosmological constant and things happening on a projection screen at infinity. But you may know better and can perhaps supply some links.

You asked about a REVIEW article. The best review is to take a look at the Loops '07 program. The plenary speaker list has representatives from almost the whole community. I suppose in 2008 we will finally see Oriti's book Approaches to Quantum Gravity: Towards a new understanding of space, time and matter(Cambridge).
It takes a book to adequately review the various approaches being worked on. But the quick overview is simple: look at the talks and abstracts of the annual conference.

http://www.matmor.unam.mx/eventos/loops07/

As you know, the Loop community is divided into many separate approaches. There are SEPARATE review articles for several of these approaches.
For QEG, look at the chapter which Percacci contributed to Oriti's book. It is on arxiv.
For CDT, google Renate Loll. I think there is also a chapter contributed to Oriti's book that is at arxiv.
For Smolin group's ball-and-tube, listen to Smolin's talk at Loops '07 which surveys the situation as of June 2007. But then refer to my PF thread "Matter as twists in geometry". I give links to two September 2007 papers by Wan and Smolin.
There is also Jesper Grimstrup's effort to put Connes Standard Model in a LQG-like context. He says he and his co-author are completing three papers that should be posted by the end of 2007, but there is no review. Grimstrup gave a talk at Loops '05 but not at Loops '07, if I remember right.
And I assume you know much of the rest---the spinfoam literature for example.

Some of these attempt a quantum dynamics of geometry PLUS detailed description of matter. Some of these approaches do NOT attempt that---they only are geometry plus nondescript generic matter fields. All these approaches are very different.

It would be very difficult to survey the whole field, except as Oriti is doing, in a book.

Demy you also brought up the issue of ACHIEVEMENTS
In English there is the saying "Don't count your chickens before they are hatched!"
You may have a Croatian equivalent (if I recall your arxiv research papers say Hrvoje Nikolic at a physics institute in Zagreb, forgive me if i have this wrong.)

In any case that is my attitude about "achievements" of various lines of theoretical research. there is no achievement until some philosophy or approach gives birth to an explicitly TESTABLE THEORY and even then the achievement is in doubt until it survives tests by which it could have been falsified.

I suppose the first test of Smolin's ball-and-tube will be with LHC, if extra dimensions are found at LHC energy then ball-and-tube is dead (topologically the underlying spatial manifold must be 3D or the knots come untied) and if SUSY is found at LHC energy then the approach is also dead because it depends on Sundance topological preon model which does not have SUSY. Smolin has bet the life of his approach on there being no SUSY and no extra dimensions. But I would still not count that as an "achievement" because the theory itself is not yet fully worked out. I am glad that you express an interest, however! I will keep you posted!

And if i hear of any kind of comprehensive review of the nonstring approaches besides Oriti's ("...Towards a new understanding of space, time, and matter") I will let you know as well. Please would you do the same, if you hear any relevant news.

Glad of your interest,

marcus

 

[BenTheMan]

In any case that is my attitude about "achievements" of various lines of theoretical research. there is no achievement until some philosophy or approach gives birth to an explicitly TESTABLE THEORY and even then the achievement is in doubt until it survives tests by which it could have been falsified.

So the fact that one can derive A/4 for black hole radiation in loops isn't an achievement?

 

[marcus]

So the fact that one can derive A/4 for black hole radiation in loops isn't an achievement?

It is a negative achievement if A/4 is wrong.
Corichi has found some quantum corrections to A/4 which should be there I believe.
Hanno Sahlmann has an interesting recent paper on that. Look him up on arxiv if you are interested, there is only one Sahlmann.

Some kind of achievement, i guess, most likely to string discredit---i.e. negative---but any evaluation has to wait for some empirical basis. Nobody gets Nobeled for pure theory :-)

 

[BenTheMan]

It will be a long time before anyone wins a nobel prize for quantum gravity, unless extra dimensions are shown to exist at LHC. Even then, there is some ambiguity about whether we're seeing, say, ADD gravity or something like technicolor or composite higgs. In many cases, the signatures are pretty hard to distinguish. This is even the case between a general SUSY model and some flavors of extra dimensional models.

I think that we won't know for sure that we have seen SUSY at LHC for quite a while, and there will be the inevitible arguments between the two camps.

On another note, I am convinced Connes is wrong about neutrino masses. The limits for a direct tree level yukawa coupling of neutrinos is 10^-8. My advisor gave a lecture on them today on neutrino masses, and this is directly from his mouth---which of course I already knew but couldn't convince you (martin) of this :) So you will have to convince me that Connes is talking about dimension 5 operators before I will believe that one can get the SM out of some non-commutative geometry.

 

[marcus]

...
On another note, I am convinced Connes is wrong about neutrino masses. The limits for a direct tree level yukawa coupling of neutrinos is 10^-8. My advisor gave a lecture on them today on neutrino masses, and this is directly from his mouth---which of course I already knew but couldn't convince you (martin) of this :) So you will have to convince me that Connes is talking about dimension 5 operators before I will believe that one can get the SM out of some non-commutative geometry.

Thanks so much for your thoughtful comments! About Connes' prediction---at least he made a definite prediction of what LHC would see based on his spectral geometry form of the Standard Model---and it would be very exciting if he were proven wrong.

Something is only real science, the saying goes, if it can be proven wrong---a real theory bets its life on an open question, and dies if something different happens from what it predicts. And real science in that sense may be, I think, the most exciting thing in life.
I will be delighted either way. Indeed if your advisor turns out right instead of Connes that would cause a bigger shakeup! Great thing about predictions is everybody wins whichever way it goes

 

[josh1]

I already knew but couldn't convince you (martin) of this

Who's martin?

 

[arivero]

you mean 10^-8 *175 GeV = 1.75 KeV?? it seems a very high limit, isn't it?

Anyway, note that Alain did all of these predictions with some caution, because they depend both on the desert and of the postulate of imposing the result at GUT level, plus the uncentainty on deciding what level GUT is, as the model does not carry supersymmetry. The numerical predictions, including the running and all that, are important for Connes's group in order to prove themselves conversant with all the process, note we are speaking here of mathematicians doing physics. He was proud about reproducing all the appendix of Veltman's book with all the signs right!

The very important point in Connes work was that the introduction of massive neutrinos forces 6 mod 8 extra dimensions.

 

[marcus]

The very important point in Connes work was that the introduction of massive neutrinos forces 6 mod 8 extra dimensions.

Barrett calls 6 mod 8 the "signature" and somebody, maybe you, remarked that it is the same as -2 (mod 8)
signature -2 is reminiscent of the signature (1, -1, -1, -1)

I was wondering which terminology you feel more comfortable with, "dimension" or "signature"?

================
I'm also wondering what figure has Connes actually predicted for the neutrino mass?

I am ashamed to say I have forgotten. I know he qualified it in various ways but forgetting about the qualifications, what was the actual figure, if there was one and you happen to remember? Or anybody, if they know?
================

Also didn't Connes predict a Higgs mass of 170 GeV? Is that reasonable? Do I have some orders of magnitude wrong?

 

[arivero]

Barrett calls 6 mod 8 the "signature" and somebody, maybe you, remarked that it is the same as -2 (mod 8)
signature -2 is reminiscent of the signature (1, -1, -1, -1)

I was just repeating some talk in the dinner table, the suggestion was not mine. But it is a good one.

Also didn't Connes predict a Higgs mass of 170 GeV? Is that reasonable? Do I have some orders of magnitude wrong?

A point here is that if you postulate you can run up to GUT scale (or down from it), the Higgs is always in the order of magnitude of these 170.

 

[BenTheMan]

you mean 10^-8 *175 GeV = 1.75 KeV?? it seems a very high limit, isn't it?

whatever units you measure yukawa couplings in. The top yukawa coupling is about 1, so that seems right for a top mass at 175 GeV. 10^-8 or 10^-10 is the limit for a dirac neutrino.

The numerical predictions, including the running and all that, are important for Connes's group in order to prove themselves conversant with all the process, note we are speaking here of mathematicians doing physics. He was proud about reproducing all the appendix of Veltman's book with all the signs right!

Perhaps you should tell martin this---I told him that Connes model seemed wrong because he predicted neutrinos with the same mass as tau leptons, then he told me that I was wrong and I should go ask my advisor.

Who's martin?

Ahh. Right. This is a different forum:) Marcus has different names on different fora, so presumably this is not the original forum where we had a discussion about Connes' SM from NC geometry.

 

[arivero]

Perhaps you should tell martin this---I told him that Connes model seemed wrong because he predicted neutrinos with the same mass as tau leptons, then he told me that I was wrong and I should go ask my advisor.

Hmm I should check (it has been one year since I heard the lectures), but I believe that the model allowed for seesaw.

 

[josh1]

With such a softened claim I fully agree.

I haven't "softened" my claim. I've explained to you what string theorists mean when they say that there is a unique theory underlying stringy physics as it's currently understood. There's just no way that these relations have no deeper physical meaning.

I also gave you tom banks point of view which I believe is more closely aligned with your own impressions and does indeed represent a more conservative position. But I also told you that his view is definitely the minority one. Nonetheless, banks is one of the worlds premier theoretical physicists and I learned a lot from his papers.

 

[BenTheMan]

Hmm I should check (it has been one year since I heard the lectures), but I believe that the model allowed for seesaw.

Perhaps. This would be the dimension five operator HLHL over a mass scale which has to be like 10^14 GeV. I didn't really understand any of the physics in the paper, only the parts that said ``neutrino coupling comprable to the tau lepton is required for such and such a cancellation''.

 

[Thomas Larsson]

"Also didn't Connes predict a Higgs mass of 170 GeV? Is that reasonable? Do I have some orders of magnitude wrong? "

A point here is that if you postulate you can run up to GUT scale (or down from it), the Higgs is always in the order of magnitude of these 170.

The Tevatron has almost excluded an SM at 160 GeV, and 170 is pretty close. Does this mean that the Tevatron may have ruled out Connes model by next summer?

 

[Thomas Larsson]

an SM <b>Higgs</b>, that is. Duh.

 

[arivero]

Perhaps. This would be the dimension five operator HLHL over a mass scale which has to be like 10^14 GeV. I didn't really understand any of the physics in the paper, only the parts that said ``neutrino coupling comprable to the tau lepton is required for such and such a cancellation''.

I see, then you argue that to seesaw a 1.7 GeV neutrino down to 0.01 eV one needs an intermediate scale, and that such intermediate scale would most probably change the renormalization group running and then the predictions, right?

 

[Demystifier]

I haven't "softened" my claim. I've explained to you what string theorists mean when they say that there is a unique theory underlying stringy physics as it's currently understood. There's just no way that these relations have no deeper physical meaning.

I agree, there must be a deeper meaning of all this. I do not necessarily agree with a conservative point of view of T. Banks. Nevertheless, I do not want to accept a definite claim on something that is not yet found.

 

[Demystifier]

So the fact that one can derive A/4 for black hole radiation in loops isn't an achievement?

I don't think one can derive it in LQG. All one can derive is that the entropy of a surface is proportional to the surface, with a universal (but undetermined!) constant of proportionality. I can hardly find this result surprising.

What IS a big achievement of LQG in my view, is the result that the theory is ultraviolet finite owing to the diffeomorphism invariance.

 

[BenTheMan]

I see, then you argue that to seesaw a 1.7 GeV neutrino down to 0.01 eV one needs an intermediate scale, and that such intermediate scale would most probably change the renormalization group running and then the predictions, right?

Well, it doesn't screw up gauge coupling unification because the right handed neutrino is a singlet and has zero hypercharge. One can give it a mass at 10^14 GeV, and then use something like the seesaw to get realistic neutrino masses.

Something else that is nice is that the mass term for a right handed neutrino explicitly breaks U(1)_{B-L} by two units. So neutrino masses are in some sense tied to this scale.

This is why people like SO(10)---you get a right handed neutrino for free, along with SU(3)xSU(2)xU(1)xU(1)_{B-L}.

I don't think one can derive it in LQG. All one can derive is that the entropy of a surface is proportional to the surface, with a universal (but undetermined!) constant of proportionality. I can hardly find this result surprising.

I agree 100%. I wish I could scale all of MY answers by an arbitrary constant :)

What IS a big achievement of LQG in my view, is the result that the theory is ultraviolet finite owing to the diffeomorphism invariance.

This is a bit confusing---marcus will complain that ``LQG'' is a generic term for non-stringy QG research, and link you to all of the talks at LOOPS 07 (the name of the conference, ironically, sort of proves your point). IF all of these approaches to QG are as different as he claims, but they are all supposedly ``background independant'', why should I be surprised by being able to find a background independant UV finite theory of QG when there are so many to choose from?

 

[arivero]

Well, it doesn't screw up gauge coupling unification because the right handed neutrino is a singlet and has zero hypercharge. One can give it a mass at 10^14 GeV, and then use something like the seesaw to get realistic neutrino masses.

Something else that is nice is that the mass term for a right handed neutrino explicitly breaks U(1)_{B-L} by two units. So neutrino masses are in some sense tied to this scale.

Ok, I see, no direct contradiction then, only that we get a new scale to justify! Talk of the desert.

 

[marcus]

Hi Ben, you seem to be carrying on a one-sided conversation with me---and giving a not-always-accurate interpretation of what I would say, and mean by it, in various cases.

the fact is that people do use "LQG" in two different senses. Demy was using it in the restricted sense, I think----the canonical approach developed mostly in the 1990s.
That's clear and fine. String-thinkers often use the word as a catch-all generic for the Loop community---the nonstring competition in general. That includes a lot of approaches that you only get an idea of if you look at Loops '07. And then they may make false statements about the nonstring competition because they don't know what it actually looks like.

I don't complain about this. It is just how people use the word. Sometimes the ambiguity can cause confusion and needs to be "disambiguated" (as the Wikipedia people say.)

Most non-string QG approaches do not currently have a BH entropy result. What Demy said seems clear, and I think it is obvious he is talking about canonical "LQG proper."

"LQG proper" does have a BH entropy result. But mathematically speaking it is not, if I remember correctly, what Demy says. I may be wrong about this but I think that according to the best current interpretation (e.g. Hanno Sahlmann and references therein) the BH entropy is NOT proportional to the area.

To first order, yes. But there are some correction terms. People have different attitudes about higher-order terms. Some dismiss them as inconsequential, others may decide they are interesting. Sahlmann is at 't Hooft's institute at Utrecht and has a pretty amazing track record for a young person---I think he is perceptive. He didn't have to look at Corichi's results (Sahlmann is good in a lot of areas and can investigate what he pleases) but he did find them interesting. So that's a cue---there might be something interesting there: in the fact that BH entropy is not proportional to area---in "LQG proper".

I could be misremembering, so I will get a link to Hanno's paper:
http://arxiv.org/abs/0709.2433
Toward explaining black hole entropy quantization in loop quantum gravity
Hanno Sahlmann
14 pages, 5 figures
(Submitted on 15 Sep 2007)

"In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this step-like behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step-length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking."

 

[BenTheMan]

Ok, I see, no direct contradiction then, only that we get a new scale to justify! Talk of the desert.

Yeah, but in this case the scale is linked to two things---neutrino masses and B-L breaking, so it's not quite so bad. One could also conceive of adding a SUSY breaking sector at this scale, giving us THREE things that are linked.

I will point out that, of course, only one of these things has been observed.