Why I am REALLY disappointed about string theory

[Fra]

I don't understand your post, Chronos, because it sounds like you consider it a flaw for a theory to rely on an unsupported assumption. That can not be right, since theories commonly do rely on unsupported assumptions, and one checks their predictions by empirical tests.

There is something especially wrong with assuming a prior 4D metric. For example it fixes the lightcone structure in an unphysical way.

I've understood that there is disagreement in these questions on here, but to speak for myself, it is NOT a misunderstanding on my behalf when extending the "background" to be MORE than just a metric.

The reason for this has also been discussed before, but to me it's about coherence of reasoning. If you take the information theoretic view where any expectation follows by counting and rating evidence, then I do not see why information about the metric, and the abstraction of metric is special and would need special treatment. After all these information and measurement perspectives wasn't around when GR was formulated. So although GR certainly has some deep lessions, it still remains to understand them in the more modern measurement setting. So far I see this has failed.

So while I respect that people disagree, I don't think it's due to confusion that people insist on the extended meaning of B/I. I just think that B/I as a scientific statement, necessarily needs to be understood different in a measurement theory, than in a classical theory like GR.

So if we say seek a deeper abstraction and understanding, in terms of information processing, at minimum we need to explain why it's ok to use any background assumption EXCEPT the metric? I'm not defening backgroundf metrics here, I'm saying that it seems that the better version of the principle really can not distinguisha between particular assumptions.

/Fredrik

 

[tom.stoer]

Tom everybody at PF can be proud of the evenhandedness and objectivity shown in much of this thread. There's stuff here worth looking back for and re-reading. But you omitted the word "not" in a sentence where I think you meant to have it. Here's a slightly edited version:

Thanks marcus for reading carefully. I corrected my statement accordingly.

 

[tom.stoer]

This thread has over 300 posts, some of which were exceptionally enlightening. Not mere bickering about appearances, public relations, obfuscation, complaints about damaged prestige etc. But really coming to grips honestly and frankly with pressing issues. Now it seems to be in a lull. What can we do? Should we go back and index the good parts? Should we make a list of posts where there is especially interesting dialogue?

Marcus, I am afraid I can't do more than indicate what the central problems and questions are which have been identified throughout the discussion (to be honest, I don't think that we found out something new; we only collected facts and questions well-known to the experts). I tried to do this a couple of times in order to focus the discussion; it could make sense to write such a short summary and conclude this thread instead of reiterate and spin in circles.

 

[mitchell porter]

How does the web of dualities (regarding different string theories) act between different manifolds and Hilbert spaces?

The very simplest case of T-duality is a closed string wrapped around a circle. There are two quantum numbers, a quantized momentum m describing the direction and speed of movement of the whole string, and the "winding number" n which counts the direction and the number of times the string is wrapped around the circle. The state (m,n) for a circle of radius R has the same energy as the state (n,m) for a circle of radius 1/R, because kinetic energy and winding energy have an opposite dependence on the radius. (references: http://ncatlab.org/nlab/show/T-duality#a_first_rough_look_4")

So in the change of perspective you do two things at once. You switch the interpretation of two quantum numbers, and you change a parameter in the background geometry (R goes to 1/R). You can get much more technical than this in describing T-duality (e.g. see the rest of reference 1), but I think that's the essence of it.

Is there a hint in certain string-related theories that the partition sum diverges due to an exponential growth of the state density? Or can one show (based on the absence of this phenomenon) that string theory is UV complete in whole theory space?

What happens at high temperatures is that long strings dominate - instead of a gas of many strings, you get one long tangled string. Also see the comments http://press.princeton.edu/chapters/s8456.pdf" , page 4-5, about UV-IR open-closed duality. The essence of open-closed duality is that you can get a cylindrical worldsheet in two ways - a closed string (circle) over a finite time interval (line segment), or an open string (line segment) over a periodic time interval (circle).

I don't actually know how UV completeness in string theory works, but those would be two of the ingredients.

 

[tom.stoer]

Regarding T-duality: I know this example and I think this is rather sound mathematically. Can we learn from T-duality how this may work for other dualities which have only been shown to be true for certain regimes?

Let's make an example: in a scale-invariant regime a toy and a real object can be identified, but leaving the scale-invariant regime this duality (identity) break down.

So one has to understand the general construction principle plus the proof; single examples may be helpful to identify the guiding principles, but what is missing is the global picture.

Regarding promises - which was one of my starting point: about 10 - 15 years ago there was the promise that M-theory is the mother of all string theories. But as I just learned the M2/M5 brane theory we have today is only another coordinate patch w/o the potential being the mother. I think that identifying further patches and related dualities will no longer be helpful to identify this mother theory.

So what one really needs in order to identify it is a unique construction principle which provides a means to understand all patches and dualities instead of messing around with one single duality.

That was the idea behind my question.

 

[mitchell porter]

Maybe we should talk about F-theory rather than M-theory, for a while? The other basic duality is S-duality, and (for IIB at least) F-theory explains it as a symmetry of the two extra dimensions (F-theory being 12-dimensional).

 

[tom.stoer]

Then the question is whether F-theory provides a better understanding of the true nature of these dualities or a hint for the underlying structure of string theory globally = including all versions / vacua etc.

Afaik F-theory is not able to achieve this; it is just another theory focussing on a small portion of theory space.

I do not say that it's not interesting to understand more about F-theory, but I would like to ask whether F-theory is the right strategy to identify an underlying mother-theory and to identify globally applicable fundamental degrees of freedom.

 

[suprised]

Afaik F-theory is not able to achieve this; it is just another theory focussing on a small portion of theory space.

True!

...to identify an underlying mother-theory and to identify globally applicable fundamental degrees of freedom.

You assume there are such things...

 

[mitchell porter]

I just found http://arxiv.org/abs/hep-th/9706155" in which he claims to derive F-theory from M-theory. "F–theory backgrounds are simply a subset of the possible M–theory compactifications." Add to that the central role that M-theory plays in the web of dualities, and I find myself reverting to the view that figuring out M-theory is the key after all.

For the string theories we have a reasonably straightforward picture (the sum over Riemann surfaces), but I don't know of anything like that for M-theory. Since M-theory has M5-branes, with M2-branes ending on strings internal to the M5-branes, the analogous construction ought to be a sum over six-dimensional manifolds (M5 worldvolumes) with internal string histories connected externally by three-dimensional manifolds (M2 worldvolumes). And just as in string theory, the "target space" in which the strings move gives rise to a 2D conformal field theory on the worldsheet (the Riemann surface), there should be a 6D conformal field theory in the M5 part of this construction, and a 3D conformal field theory in the M2 part, which corresponds to the geometry through which the M-branes are moving. But I've never seen anything like this. Then again, even if it is a valid and tractable construction, you couldn't make it work unless you had figured out the M-brane worldvolume theories, and that's work in progress.

http://arxiv.org/abs/0905.2720" has something about the 6D theory, though I think it's somewhat simplified from its full, physically relevant form - see the remarks on page 13 about "more elaborate constructions".

 

[MTd2]

I thought that 6D theory from witten was not related to M5 branes, but just a theory with not much relation to physics. I mean, that is a N=2 theory, right?

 

[mitchell porter]

No, it really is supposed to be the worldvolume theory of the M5-brane. There's a lot of recent work in which N=2 4D theories are derived from the 6D theory compactified on a Riemann surface (see "Gaiotto duality"). The D3-brane of IIB / F-theory is an M5 compactified on T^2, and shows up in the F-theory GUTs (http://arxiv.org/abs/1006.5459" ).

I think the best papers to read, for progress regarding M-branes, might be those by http://arxiv.org/find/hep-th/1/au:+Berman_D/0/1/0/all/0/1". 0710.1707 reviews the situation on the eve of the M2-brane "minirevolution", and can be supplemented by, e.g, Pei-Ming Ho's 0912.0445. Berman's most recent (1008.1763) even brings U-duality groups into the picture, and so begins to make contact with the school of thought which would derive M-theory from an E10 or E11 symmetry.

 

[atyy]

No, it really is supposed to be the worldvolume theory of the M5-brane. There's a lot of recent work in which N=2 4D theories are derived from the 6D theory compactified on a Riemann surface (see "Gaiotto duality"). The D3-brane of IIB / F-theory is an M5 compactified on T^2, and shows up in the F-theory GUTs (http://arxiv.org/abs/1006.5459" ).

I think the best papers to read, for progress regarding M-branes, might be those by http://arxiv.org/find/hep-th/1/au:+Berman_D/0/1/0/all/0/1". 0710.1707 reviews the situation on the eve of the M2-brane "minirevolution", and can be supplemented by, e.g, Pei-Ming Ho's 0912.0445. Berman's most recent (1008.1763) even brings U-duality groups into the picture, and so begins to make contact with the school of thought which would derive M-theory from an E10 or E11 symmetry.

Great, thanks for the recommended reading! The E10,11 stuff is really intriguing, but I've always wondered if it's applicable only in the vicinity of a spacelike singularity.

 

[MTd2]

No, it really is supposed to be the worldvolume theory of the M5-brane.

It was not really a yes/no question. Actually, I wanted to know why M5 branes should be N=2 instead of N=1 like SUGRA 11d. Why?

 

[mitchell porter]

Enhanced supersymmetry is a common phenomenon, e.g. N=8 d=4 SUGRA is N=1 d=11 SUGRA compactified on S^7. I don't have anything insightful to say about the M5-brane case but see page 9 of http://www.ggi.fi.infn.it/talks/talk1782.pdf" .

 

[MTd2]

Enhanced supersymmetry is a common phenomenon, e.g. N=8 d=4 SUGRA is N=1 d=11 SUGRA compactified on S^7.

Those are compactified theories, but if it is a source of a theory, like M5, it should be expected to have the same number of supersymmetries, right?

 

[mitchell porter]

We need to distinguish between "number of supersymmetries" and number of supersymmetry generators. See http://en.wikipedia.org/wiki/Supersymmetry#Extended_supersymmetry". The rule of thumb is that in dimension d, N=1 supersymmetry has 2^d/2 generators if d is even, 2^(d-1)/2 if d is odd (because of the size of spinors in the different dimensions). So N=1 d=11 has 32 supercharges; N=1 d=4 has just 4 supercharges; and a 32-generator susy algebra in four dimensions therefore consists of eight copies of the N=1 algebra, i.e., it's "N=8".

For the M5-brane: The 11d bulk has 32 supersymmetries; half of them are lost in the projection onto the 6d worldvolume; but that's still twice the number of supersymmetries in N=1 d=6, which by the formula above has just 8 generators. So that's where "N=2" comes from, for the M5-brane.

Those are compactified theories, but if it is a source of a theory, like M5, it should be expected to have the same number of supersymmetries, right?

That's something for which I don't have any insight - how the doubling of supersymmetry comes about, from brane to bulk, if you take an "M5-centric" view of things.

 

[suprised]

A brane is a background configuration that spontaneously breaks some of the translational symmetries because it is localized. This applies to the supersymmetries as well, and depending on the configuration, only 1/2 or 1/4 or 1/8 or 0 of the supercharges survive. Spontanous breaking means that the full symmetry is still there, albeit the broken part is non-linearly realized.

From the viewpoint of the world-volume of a brane, the broken translational symmetries manifest themselves as massless scalars, which represent the goldstone modes for those broken symmetries (and which realize the broken symmetries in a non-linear way). For the broken supersymmetries this works analogously, except that the goldstone modes are fermions; they realize the broken supersymmetries in a non-linear way.

For some info, see eg p3 in: http://arXiv.org/pdf/hep-th/0011018v1
and here: http://arXiv.org/abs/hep-th/9612080

 

[MTd2]

I am more or less aware about this issues. The point I am trying to make it is how many supersymmetries I should expect from M5 branes if that is a fundamental object.

For example, Mitchell Porter wrote:

"For the M5-brane: The 11d bulk has 32 supersymmetries; half of them are lost in the projection onto the 6d worldvolume; but that's still twice the number of supersymmetries in N=1 d=6, which by the formula above has just 8 generators. So that's where "N=2" comes from, for the M5-brane."

Would that reasoning work for finding the number of supercharges the fundamental strings? In case that is not true, why should I expect that to work with M5 branes, which are also fundamental?

 

[mitchell porter]

There is a relationship between worldsheet supersymmetry and spacetime supersymmetry in string theory too. But these relations are all rather complicated. It's like the classification of Lie algebras, there's a logically determined pattern but it's not simple. At least it's not simple for me. I am reduced to just quoting from a few papers.

"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 are a number of different branes in string theory and M-theory, most conveniently characterised by their field content when seen as a field theory on the world-volume. The simplest ones, the so-called p-branes, have a scalar multiplet on the world-volume. D-branes contain a vector multiplet, coupling to string endpoints, and the M5-brane has a self-dual tensor." -- http://arxiv.org/abs/hep-th/0105176"

And http://arxiv.org/abs/hep-th/0301005" is a highly efficient review of susy and sugra theories in 4 to 11 dimensions.

 

[MTd2]

So, probably the fundamental object of m-theory has N=2 Supersymmetry, right? And M2 has N=1 supersymmetry?

 

[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.