Why I am REALLY disappointed about string theory

[tom.stoer]

let me interrupt you for a moment; the discussion is very interesting, but does it tell us anything about the true fundamental object in string / M-theory? is this the idea behind "the fundamental object of m-theory has N=2 Supersymmetry ... and M2 has N=1 supersymmetry"?

 

[MTd2]

Tom, I have some ideas to post here... I just need the answer to know if M5 has N=2 SUSY and M2 has N=1 susy :)

 

[mitchell porter]

The worldvolume theory for M2-branes can have very high supersymmetry, e.g. N=8 for BLG and N=6 for ABJM.

 

[MTd2]

What is expected to be fundamental, N=8 or N=6? Only one can be true, right?

 

[mitchell porter]

N=6 occurs on orbifolds, so N=8 looks more fundamental in some sense.

 

[MTd2]

Are you aware if anyone tested if SUGRA 11d is asymptotic safe?

 

[suprised]

Well indeed I agree with Tom that this thread runs off-topic.

But still I feel inclined to comment on this one, in order to fight misinformation in the following paper.

"In string theory, the interplay between worldsheet symmetries and their consequences in spacetime remains largely mysterious. Certain results, however, indicate strong connections between the two. For example, it is well-known that N = 4 supersymmetry on the worldsheet implies N = 2 supersymmetry in spacetime, and likewise it has been demonstrated that N = 2 supersymmetry on the worldsheet implies N = 1 supersymmetry in spacetime." -- http://arxiv.org/abs/hep-th/9505194"

There is nothing mysterious, though it seems to the author of that paper. The point is that SUSY is determined by the background, and not so much by the world-sheet theory. World-sheet susy is necessary for space-time susy (in order for being able to construct the supercharges) but not sufficient. There is an extra condition necessary, which depending on the language one is using, can be phrased "charge integrality" or "vanishing first chern class" (actually things are more subtle with "generalized geometries" but let's keep it simple).

In fact there are many theories with world-sheet susy but not space time susy; an example exists even in d=10, there is the so-called O(16)xO(16) heterotic string which is not susy in space-time but on the world-sheet (for whatever reasons, this and other similar models are almost never discussed when talking about string dualities in 10d). So the sentence "and likewise it has been demonstrated that N = 2 supersymmetry on the worldsheet implies N = 1 supersymmetry in spacetime" is manifestly wrong, the implication goes the other way.

 

[Haelfix]

Are you aware if anyone tested if SUGRA 11d is asymptotic safe?

Doubtful, since the UV completion is decidedly stringy and one can show that there are extended objects in the nonperturbative spectrum of the theory (pbranes and so forth)

 

[MTd2]

But I said that because SUGRA 11d is perturbatively non renormalizable. And how can it be stringy if strings are not an object of this theory?

 

[Haelfix]

Strings are not pertubative objects in the theory. However there are charged black hole solutions that otherwise do exist. These are the objects that are identified with the BPS branes in the suitable limit. Consequently, when you take the classical theory and apply consistent quantization conditions/unitarity checks you will find that the supergravity theory must be either completed to the full Mtheory or already include all of the objects as asymptotic states.

I'm pretty sure that this is by now pretty much textbook.

 

[MTd2]

But the exact nature UV completion is not known. So, why not checking if SUGRA 11d is enough by itself using asymptotic safety? Maybe SUGRA 11d is the M-Theory.

 

[tom.stoer]

But the exact nature UV completion is not known. So, why not checking if SUGRA 11d is enough by itself using asymptotic safety? Maybe SUGRA 11d is the M-Theory.

That will neither be easy nor sufficient.

• in SUGRA you lose the heavy string states; you have to explain what / where they are or what the corresponding effects are
• asymptotic safety is not able to scan the whole theory space; you must explain why only the lowest order interactions survive (in GR you can construct f(R) theories nearly w/o restriction; what about these higher order terms in SUGRA? why do they vanish?)
• asymptotic safety is not able to tell you how many fix points you have
• even if this whole program works I doubt that the perturbation series will converge; usually one would expect that its sum is divergent (finiteness order-by-order is not sufficient)

Anyway: it's a nice idea and it fits to some thoughts I had a couple of years ago: why shouldn't string-/ M-theory be a class of effective theories instead of the fundamental theory? perhaps the strings and branes are non-perturbative effects of an underlying SUGRA / gauge theory?

At least at the level of the action SUGRA seems to be "more unique" than string theory. Perturbation theory is better understood (in string theory it's rather mysterious: everybody expects that it's finite even though not even the n-loop measure has been defined; in SUGRA the measure is defined, what remains to be done is to prove finiteness).

Perhaps one should turn things round!

 

[MTd2]

That will neither be easy nor sufficient.

But my sugestion is not about being enough, but about being necessary! :D

Is it possible that m-theory does not have the concept of supersymmetry at all in its fundamental level?

 

[tom.stoer]

As I don't know what M-theory _really_ is, I can't tell

 

[MTd2]

Hmm, but the question was about what it is not. It is not a unicorn or a flying saucer. So, is it possible that it does not have susy?

 

[tom.stoer]

you does susy emerge from nothing?

 

[atyy]

you does susy emerge from nothing?

http://arxiv.org/abs/1009.5127 ?

 

[MTd2]

you does susy emerge from nothing?

For example, what if M=2 branes were not supersymmetric?

 

[tom.stoer]

Thanks; I'll check it.

Can we then come back to the ideas of MdT2 and me from post #361& #362?

 

[Haelfix]

Hmm, I am not following at all. I think you guys are a little confused about a few things, so let's back it up a few steps.

"But the exact nature UV completion is not known. Maybe SUGRA 11d is the M-Theory. "

The d=11 supergravity *is* the classical limit of Mtheory. Conversely the consistent quantization of Maximal Supergravity yields Mtheory nonperturbatively, so yes it is known.

The point is, you can;t really think about one without the other so long as you are interested in the UV limit. This was part and parcel of the 2nd superstring revolution b/c all of a sudden the various webs of dualities were elucidated utilizing the 'microscope' of d=11 supergravity (which had been studied independantly for 20 years)

Now proving this limit in both directions is hard but doable (at least handwavey).. see eg
http://arxiv.org/abs/0704.0777

and the conversations
http://golem.ph.utexas.edu/~distler/blog/archives/001235.html

http://motls.blogspot.com/2008/07/two-roads-from-n8-sugra-to-string.html

which deal with the dimensionally reduced theory.

 

[MTd2]

But those are links about the non dependence on string theory of N=8 d=4 SUGRA for perturbative renormalization. And what is the consistent quantization of d=11 supergravity if m theory is not known?

 

[Haelfix]

What do you mean by 'M theory is not known'? What do you think all the matrix theories are about?

Reread the links again. The paper I provided was an argument for something even stronger, namely the nondecoupling of string theory from maximally extended supergravity for d>=4.

Its only for d=2, and d=3 where things are qualitatively different (the stringy states develop enormous masses and can presumably consistently decouple)

Of course the interesting case is the dimensionally reduced d=4 theory, b/c it might be perturbatively finite. Which is theoretically interesting, b/c that would imply that the stringy states don't arise merely from completing the theory, but actually are there to begin with (see Jacques discussion).

 

[tom.stoer]

@Haelfix: I think we get back to the old confusion what M-theory is.

The whole discussion was about a means to identify the true, unique underlying degrees of freedom of string theory. During the second superstring revolution Witten coined the name M-theory for the (to be constructed) mother of all string theories. So the expectation is that M-theory does the job and provides something like a unique action (or whatever).

In the meantime it became clear that one is not really able to construct this M-theory. We discussed several approaches here (especially the M2/M5 brane theory), but we agreed that this is not M-theory in the above mentioned sense but only another subset of the theory space. Some time ago it has been asked if matrix theory could be M-theory (in the above sense); I do not remember the details but I think the conclusion was that matrix theory is not able to do the job b/c it exists only in a certain limit. So in addition to the well-known string theories we have 11d SUGRA, we have this M2/M5 guy and we have matrix theory. But none of them is M-theory.

I am confused about you statement

The d=11 supergravity *is* the classical limit of Mtheory. Conversely the consistent quantization of Maximal Supergravity yields Mtheory nonperturbatively, so yes it is known.

What do you mean by "classical limit"? How can you derive a classical limit of a theory that is still not known? How does this "consistent quantization" of SUGRA look like? What is its action, its path integral, its Hamiltonian? I think this consistent quantization is not known; otherwise the while program would have been succeeded - but as we know it's still work in progress.

 

[tom.stoer]

I am afraid we are running in circles and we are partially confused as we do not know enough about all the magic relationships between the different theories (this is at least true for me).

Question: is there a detailed and consistent map of the theory space known so far?

I do not mean something like http://upload.wikimedia.org/wikipedia/de/thumb/2/2c/M-Theory.png/300px-M-Theory.png as it is partially misleading.

• It should list all theories
• It should provide a notion for the relevant degrees of freedom (open/closed strings, M2/M5 branes, matrices - which one?,...) for each theory
• It should provide a small set of fundamental equations for each theory (action, ...)
• It should list all relations (the self-duality is missing in this picture)
• Each relation should be qualified like "S" with the appropriate couplings, "low energy", "classical limit" - with an explanation what that means, ...
• It should distinguish between different theories; it should especially not list one central M-theory as we know that this is stll a hope; instead it should show M2/M5-, matrix-theory etc. ...

I guess there isn't such a map - otherwise it would have been posted here. Is there a chance to construct it here in this forum? e.g. as a simple table?

 

[Haelfix]

Whenever we talk about M2 and M5 branes, and d=11 supergravity, chances are the discussion is tacitly about Mtheory in the more restricted sense (eg not the whole configuration space of string theory). This 'restricted' entity is pretty well studied and you can come at it (again using dualities) from a variety of different directions.

Incidentally, I don't like to use the word 'theory' for the different corners and formulations of string theory b/c typically it causes confusion in the sense that there is really only *one* string theory. It is unique as a theory just like maximal supergravity is, and similarly both have a number of possible compactifications and a landscape of solutions.

"What is its action, its path integral, its Hamiltonian? I think this consistent quantization is not known; otherwise the while program would have been succeeded - but as we know it's still work in progress. "

The supergravity action is well defined, and the quantization thereof has been studied long before string theory. Mtheory (in the restricted sense) does not have an obvious action (its difficult to write one down for membranes), however you can study it somewhat indirectly using the many different dualities. So the point is we know it exists, and theoreticians can even formulate it with matrix theories to give it a precise definition, observables and so forth.

 

[MTd2]

Reread the links again. The paper I provided was an argument for something even stronger, namely the nondecoupling of string theory from maximally extended supergravity for d>=4.

But we are talking about 11d and superstring theory goes up to 10. More than that is the other way aroung, supergravity yielding superstring.

Mtheory (in the restricted sense) does not have an obvious action (its difficult to write one down for membranes), however you can study it somewhat indirectly using the many different dualities.

We are not arguing here for its existence but for what is it`s direct formulation, as you put it. I proposed before to see if maximal supergravity in d=11 is the formulation and not a low limit.

 

[Haelfix]

Incidentally, one of the running difficulties with talking science on this particular board is that the steps and logical inferences taken are enormous and can be horrendously confusing, even to experts. We are shortening many papers worth of calculations into simply diagrams and words, but rest assured there are many subleties and this is by no means trivial.

I mean we're sitting here talking about maximal supergravity in 11 dimensions and somehow I doubt that many people discussing it, actually have much practical knowledge of it. For instance, how many people have studied the classical charged black brane solutions? Seriously, its hard to make sense of anything if you don't know what they look like.

How many people have actually gone through a Kaluza-Klein reduction in detail in just a simple GR context? None of this makes any sense at all, unless you do the baby steps and the homework problems first, before tackling the stuff that the experts look at.

When we talk about quantum objects where no lagrangians exist, it definitely strikes a nerve if you haven't seen it before. Of course if you go through Di Fransesco and do the necessary homework in conformal field theory, well then it becomes a little less perplexing.

 

[Haelfix]

But we are talking about 11d and superstring theory goes up to 10. More than that is the other way aroung, supergravity yielding superstring.

Again, I don't know what to make of this statement. Mtheory has an additional dimension, a sort of infinitesimal one and is dual to the strong coupling limit of Type IIA as well as having d=11 supergravity as its low energy classical limit..

I just argued that you can't think of d=11 supergravity and somehow consider it apart from *string* theory (by that I mean M theory in the restricted sense). Whether one yields the other is analogous to thinking about the the Fermi theory of the weak interaction and the modern electroweak interaction. In order to make sense of the former you need the latter to complete it, and the latter reduces to the former in the appropriate limit. Good?

 

[tom.stoer]

Let's look at QCD again. We know its elementary degres of freedom (quarks and gluons) and we can do calculations (in all known regimes!) based on these degrees of fredom exclusively. Of course in the low-energy regime effective pion/nuclean theories may be easier to handle, but in principle the fundamental degrees of freedom are sufficient. That means there is no "completion" of QCD requiring new degrees of freedom for mathematical consistency. QCD itself is already complete!

What we try to do here is to find exactly such a description for string-/M-/theory/SUGRA. I think we need not care about the fact there are non-perturbative aspects that may be described by new degrees of freedom - as long as they are not equally fundamental. I do not believe that branes in string theory are fundamental degrees of freedom in that sense; they are just a way to parameterize a solution and act with (perturbative) excitations on top of them. That does not automatically mean that one has to include them into the fundamental picture, only that the fundamental picture has been broken by splitting the theory in a "solution" plus "perturbations"; it's the approximation that causes the trouble, not the theory itself.

Again QCD: there is no reason to use instantons as fundematal degrees of freedom even if it's reasonable to study the propagation of a quark in an instanton liquid.

In this spirit I am asking for the fundamental degrees of freedom of string-/M-theory/SUGRA. And that's why I am with MTd2: isn't it possible that 11d SUGRA already provides this fundamental picture? Why not?

 

[MTd2]

I just argued that you can't think of d=11 supergravity and somehow consider it apart from *string* theory (by that I mean M theory in the restricted sense). Whether one yields the other is analogous to thinking about the the Fermi theory of the weak interaction and the modern electroweak interaction. In order to make sense of the former you need the latter to complete it, and the latter reduces to the former in the appropriate limit. Good?

Not good, because I didn't cosider 11-SUGRA apart from string theory. I just asked if 11-SUGRA could be THE m-theory in case it is asymptotic safe. String theorists uses a lot of different mathematical methods. Why not this one?

 

[mitchell porter]

So the sentence "and likewise it has been demonstrated that N = 2 supersymmetry on the worldsheet implies N = 1 supersymmetry in spacetime" is manifestly wrong, the implication goes the other way.

I assume your disagreement is with the manner of Dienes's statement - the way he states things, the way he puts the worldsheet first - because I don't know any concrete counterexamples to what he says. Think of his propositions as folklore summarizing a variety of case studies. Do you have an example (maybe the O(16) x O(16) theory? actually Dienes wrote http://arxiv.org/abs/hep-th/9707148" ) where the worldsheet has N=2 susy but spacetime does not have N=1 susy? I think also that when he says the relationship is mysterious, he means it is complicated - that no simple explanation is known which would explain all the cases covered by the folkloric generalization.

 

[suprised]

Do you have an example (maybe the O(16) x O(16) theory? ...where the worldsheet has N=2 susy but spacetime does not have N=1 susy?.

Yes O(16) x O(16) is a counterexample. There are zillions others one can generate via a computer, eg in d=4. The conditions under which space-time susy arises are very well understood since the eighties (I mean the traditional way, there have been generalizations more recently using flux backgrounds). Unfortunately, this issue (like so many others) has been confused by misleading or imprecise or wrong statements, like the one alluded to above. World-sheet susy is necessary for having fermions in space-time; space-time susy only arises when extra conditons are satisfied, either algebraically or geometrically, which are simply the existence conditions of conserved space-time supercharges.

But again, this is a side track of the current main topic, so the profile should be kept low; as if the main topic woulnd't be enough confused by itself...

 

[MTd2]

But again, this is a side track of the current main topic, so the profile should be kept low; as if the main topic woulnd't be enough confused by itself...

No, this is very on topic. The disagreement over very basic definitions or what has been achieved to get to that point is a huge disappointment. Just write down the definitions and point to where one will be able to understand it.

 

[suprised]

Disappointment over what? There is no disagreement among the experts of how susy arises in string theory. That's a completely minor, well-understood side point here in this context of the meaning of M-theory.

 

[Haelfix]

"isn't it possible that 11d SUGRA already provides this fundamental picture? Why not?"

No it is not possible! QCD is a renormalizable asymptotically free theory, so it makes sense by itself to arbitrarily high energies.

D=11 supergravity is nonrenormalizable and needs a UV completion just like the Fermi theory does. (Mtd2, ask yourself why the Fermi theory is not asymptotically safe for an analagous answer)

New degrees of freedom will become important to ensure consistency, namely the ones from Mtheory.

Now, you might ask, is the UV completion unique, and that's a harder question to show. Going the opposite direction is easy to show, but in principle one would like to be able to bootstrap their way up from the supergravity theory to derive the full stringy states. You are free to ask an expert about that.