Why I am REALLY disappointed about string theory

[MTd2]

I blame it on Marcus & Co.

 

[tom.stoer]

That's not the point: I had something in mind when I started this thread. I knew that it would become difficult. Therefore using "killing" was counter-productive, unrewarded and wrong.

 

[marcus]

I blame it on Marcus & Co.

Marcus & Co. loves and admires string. We have never criticized string mathematics. Why should we?
Personally I just report the news

But MTd2, let's not talk about each other! Tom has started a great thread. I am really interested in what people like Negru have to say that are actually embroiled in the string business. Maybe like Christine I will try to stay in the background and listen to others' opinions.

 

[marcus]

I had something in mind when I started this thread...

I will be sorry if my butting in somehow contributed to stalling the thread.
The initial series of exchanges between you and Negru was refreshing and constructive. Negru is a good spokesman: forthright honest un-defensive comparatively uncomplaining. I'm hoping to hear that conversation continue in some form, with the same or different parties, sometime soon.

There was also a mot juste metaphor about shampoo and justice,
a few words of which I copied and pinned to the wall of my computer space.

Of course I am prepared for answers regarding landscapes (Susskind) and mathematical universes (Tegmark). But frankly: I will never accept these arguments. This is regarding string theory, therefore I expect answers in the context of string theory (if my daughter has to go upstairs in order to shampoo I don't accept discussions regarding justice; that does not mean that I am unintersted in justice - I am - but not in the context of telling a six-year old girl to go upstairs in order to shampoo!)

 

[tom.stoer]

Hey marcus!

You like it? Good on you - and me :-)

Back to strings and to my intention. We had a couple of discussions here (and I was involved) where we discusses pros and cons of string theory. Unfortunately most threads ended with a variation of "string theory is unphysical" and "why can't you see that string theoriy is a great theory".

My impression was that were are (at least partially) unfair. We judged string theory from the perspective of completed or "working" theories although we should know that it isn't. (This become clear in this discussion a couple of times). So we should be fair and try to apply different standards. Nobody here knows how it felt 100 years ago when great physicists where looking for a solution of the quantum puzzle; maybe similar; one knew that there was something out there, but what exactly nobody could say.

So my conclsuion was that we (skeptics) should accept that string theory is work in progress and should listen to the argments of the string community carefully (we are no Woit's here :-).

But on the other hand the string community should accept some standards as well (at least for THIS discussion). Namely that one should not constantly change the rules of the game. That's why I was insisting on not talking about new standards in science, landscape and things like that. To be honest: it can very well be that string theory stays "unpredictive" in this sense; but (once proven) to overcome this situation is not a matter of string theory itself. It is really a matter of physics (as a whole). If string theory predicts that it cannot make predictions except for the prediction of the landscape, then we need a different and a larger context to deal with it. I do not say that I am not interested in this discussion, but not in the context of string theory - seen as an ordinary but still developping physical theory. Especially as I learn that string theory is work in progress and it may therefore very well be that there are clever ideas beyond the landscape to be discovered ... So I try to limit (focus) the context of this discussion - nothing else (and so far it worked, that's why perhaps it may have been better not to write this paragraph :-)

My conclusion was that it should be string theorists themsevles to assess string theory according to its value and its inherent problems. This is what I am still asking for.

 

[mitchell porter]

How I think about the string landscape:

First we need to find some vacua that do give us the particle-physics standard model and cosmological standard model (perhaps with some extra features). Remember that even that much has not been done! There are vacua which look like the MSSM, but no-one seems to have exhibited a construction providing the exact masses of the observed particles. It's all still work in progress.

Then, we need to embed this in a cosmological solution to string theory. I don't hold much hope for the idea of a unique, dynamically determined vacuum. The viewpoint of eternal inflation, with different regions of space exhibiting different particle spectra etc., seems like a natural cosmology for a theory with many different vacua. What's important is to show that this really is the natural cosmology of string theory.

In this regard, Susskind's original landscape paper (hep-th/0302219, pages 4-5) has a simple and vivid description of a string cosmos containing regions in different vacuum states. It's 11-dimensional M-theory, compactified on a 7-torus, leaving 3+1 large dimensions. The fundamental 5-brane of M-theory couples to a magnetic 7-form field. If you consider these branes and fields wrapped on 3-dimensional subspaces of the 7-torus, you are left with a 2-dimensional object coupling to a 4-form field in the 3+1 large dimensions. These 2-dimensional objects (partly compactified M5-branes) are then domain walls interpolating between regions of 3-dimensional space where the 4-forms take different values.

I presume the cosmological reality is more complicated than that, but it offers a starting point for thinking about the big picture.

 

[tom.stoer]

I agree that one has to come much closer to the xMSSM; but in parallel one has to find xMSSM at the LHC, otherwise the theoretical progress in string theory has no value.

 

[humanino]

I agree that one has to come much closer to the xMSSM; but in parallel one has to find xMSSM at the LHC, otherwise the theoretical progress in string theory has no value.

What happened to the misaligned superstring ?

 

[friend]

Isn't string theory about how strings and membranes vibrate on an pre-existing spacetime background which is just assumed? If so, then string theory is not background independent. Is this the reason for the landscape problem?

 

[tom.stoer]

Isn't string theory about how strings and membranes vibrate on an pre-existing spacetime background which is just assumed? If so, then string theory is not background independent. Is this the reason for the landscape problem?

I was thinking about that - and I hesitated to include the background-dependency into my list of questions and open issues. We had this discussion a cpouple of times and we came to the conclusion that string theory may be background independent - but not in the sense as excpected in ART.

I have a different opinion on the landscape: I guess that a completely different structure will emergy once one is able to perform full non-perturbative calculations. But this is implicitly assumed when a talk about a final set of definitions of the theory - which is currently missing.

 

[BenTheMan]

tom, et al.---

Expect a longer response to your questions in the near future, but let me make a point quickly that most people don't acknowledge.

The MSSM has a landscape problem.

Let me clarify: when I say ``landscape problem'', I'm not referring to cc problems (which no body can solve). I mean a much more mundane issue, involving scalar VEVs. I claim that any theory in which couplings and masses are set dynamically will exhibit a landscape of solutions, if not at tree level, then certainly when one considers higher dimensional operators. Let me explain.

One of the ways to understand the landscape problem in string theory is to note that string theory is a very good way to get SUSY QCD theories, which have a consistent UV completion. But any SUSY QCD theory with chiral multiplets (i.e., fermions that aren't gauginos) has a landscape problem: the reason is because one can always write down a set of supersymmetric solutions to any theory, called F=0 and D=0 constraints. In a broad class of theories, when F=0 and D=0 solutions exist, they're not unique. Thus there are a continuum of possibilities that comes just from the presence of supersymmetry.

Now, let's assume that the supersymmetry isn't broken in our universe. What does the landscape look like? Well, we have all these scalars in our theory, called sfermions (squarks and sleptons) which obey some F=0 and D=0 constraints. These F=0 and D=0 constraints can be satisfied at points where the squarks get VEVs. This means that SU(3) is broken, which is ruled out by observation (to say the least).

Thus we live in a very particular vacuum of nature: that is, all scalar VEVs, with exception of the higgs, are zero. The fact that other vacua exist where the SM gauge group is broken is a fact that follows from field theory, and NOT string theory.

You can extend this argument to any theory with scalars. This is a particle physics statement, and has nothing to do with quantum gravity.

To emphasize this point, consider the Higgs. The higgs mass is the only dimensionful parameter in the SM, and it sets the scale for electroweak symmetry breaking, and all of the fermion masses. The higgs potential in the SM is ad hoc, and has no known origin. In fact, if we write down some higher dimensional operators, as would arise from some Wilsonian effective theory, it's not hard to imagine that we might find other minima for the higgs. So in the full theory (some GUT, say, or---at worst---some non-stringy QG model) the higgs potential can have many minima. So it's even possible that the SM has a landscape problem.

The point is, the string theory landscape is nothing new, and was even realized a long time ago. The only reason it's a problem now is that some people are jealous that their pet theories are being ignored by serious scientists. You know---it's always easier to sh1t on someone else's work than to convince people that your ideas are worth listening to, or even come up with your own ideas in the first place. And make no mistake---QG researchers are actively involved in the former, and Columbia University professors who don't have their own research program actively engage in the latter.

It is true that string theory was overhyped. But this is the tendency of the media to sensationalize results. Remember the hoopla involved with Garrett Lisi's E8 paper a few years ago? Discover Magazine had a list of ``10 Successors to Einstein'', and this paper landed Lisi on that list. Good for him, but you can ask him yourself if he believes he should be there. Where were all the stories pointing out the objections of the scientific community of his work? Did you see any rebuttals? I didn't. Journalists, by and large, are idiots. (If you need proof of this, read this article, published in a ``serious'' pop science mag.) They want headlines, and physicists want money. So it's an easy tradeoff to make---we get publicity, and they get a story. Anyway this is sociology and not physics, so it's not really worth talking about.

Let me say that I hope (as much as anyone) that a unique solution exists. But I also understand why the solutions may not be unique---I have spent my (short, and rapidly winding down) career as a string phenomenologist, and I can see the types of problems people tend to have in ALL string constructions.

Let me finally reiterate and old argument: Citing the landscape as a problem may just come from the fact that people are expecting too much from string theory. Who are WE to expect that Nature is unique? Does this bother you? At some point, people tried to derive why we have 8 planets around the sun, or why Earth was some particular distance from the sun. But there are trillions of suns and Earth's, so is it worth while to try and understand why THIS earth-sun system happens to be the right age, and have the right separation for liquid water and a comfortable temperature? If you are a creationist, then you might marvel at this fact and spend time thinking about it---that is, if you believe that there's some reason for it all, then you will waste time on this problem. But if you understand that anthropics is the reason that humans live on earth, you ask different questions altogether.

 

[friend]

I was thinking about that - and I hesitated to include the background-dependency into my list of questions and open issues. We had this discussion a cpouple of times and we came to the conclusion that string theory may be background independent - but not in the sense as excpected in ART.

So string theorists believe that there may be only one background consistent with the physical constants we observe?

 

[negru]

Had a longer answer eaten..so I'll summarize some points.

Like marcus said, string theory at the moment is huge. It has quite a few applications ( f theory, ads/cft, black holes, etc). I personally find it unlikely that you can just expect to compactify some 10D theory and get the SM, then use ads/cft to compute some qcd stuff, use twistor strings to compute tree level qcd (topological strings are just as much strings as M theory is), etc and never make a deeper connection between these things. How could the real world be just a holographic projection of higher dimensional string theory, AND at the same time actually made of tiny strings at high enough energy? I mean, if gluons are actually strings, via ads/cft, you get another string/string holographic duality or what?

As has been pointed out, we don't have a working definition of string theory (one which explains why these things work). How could it predict anything if we don't know what it is?

That's why questions like "is string theory falsifiable" or "if there is no susy does it kill string theory" or "did it predict anything yet" etc always irritate string people. Not because they're inherently silly (these are the questions I was asking myself when deciding what path to choose), but they're just not well posed. We don't know enough string theory to ask the right questions.

And if you'd like to get rid of string theory, you'd have to separately kill all of these seemingly unrelated applications, since they use different assumptions. Also, about susy/high D being "physical". Physical to me means only something we can measure. Internal machinery, like hilbert spaces, we can never measure. However this doesn't stop them from making predictions. So for example if we go to Planck energy scales, don't find any strings, this won't mean ads/cft is wrong.

 

[MTd2]

You know---it's always easier to sh1t on someone else's work than to convince people that your ideas are worth listening to, or even come up with your own ideas in the first place. And make no mistake---QG researchers are actively involved in the former, and Columbia University professors who don't have their own research program actively engage in the latter.

You mentioned 3 types of people but you just qualified 2 of them.

 

[BenTheMan]

You mentioned 3 types of people but you just qualified 2 of them.

I am glad to see that you really understood the content of what I was talking about. You know---I come to this forum so that I can occasionally put in my two cents about things that I am interested in, or have thought about. It is truly rare that I meet someone who really gets me, at such a deep level.

Are you single?

 

[MTd2]

Hmm. Well, today I am pretty tired, so I am really slow, so I had to ask. But I am detecting some irony now... But no, I am not single.

 

[suprised]

So string theorists believe that there may be only one background consistent with the physical constants we observe?

Since this is thread is about getting out of control as well, I still need to read through all the answers and elaborate on some answers to Tom. But right now I don't have the time, though this question stroke me as separately commentable.

One thing that never comes out clearly in such discussions is that there is not "the" string physicists as a block with one fixed opinion. In fact there is a lot if arguments going on within the community, and it is split especially on this one. So I can answer only for myself; and my opinion is very clear on that. Namely it is quite inconceivable that the extremeley narrow range of parameters that allows us to exist, fits precisely to the only consistent background (of any theory). This is a bit like believing that the DNA molecule that defines us, is the unique solution of some fundamental theory, rather than being just a particular solution to a unique theory (electromagnetism in this example).

Edit: I just noticed that I might have misread the question. Well be it as it is.

 

[tom.stoer]

As has been pointed out, we don't have a working definition of string theory ... How could it predict anything if we don't know what it is?

That seems to be the conclusion of the discussion. So demanding that the theory shall produce physically falsifiable predictions shall be postponed as long as there is no sound definition.

That's why questions like "is string theory falsifiable" or "if there is no susy does it kill string theory" or "did it predict anything yet" etc always irritate string people. Not because they're inherently silly ... but they're just not well posed. We don't know enough string theory to ask the right questions.

I understand that these questions can irritate people; but we should neither blame the questioner nor the question but the theory. Look: I tried to ask physical questions, independent of any specific technical detail. I did not ask for details regarding compactification on a specific M⁷ in M-theory. I did not ask regarding mathematical proofs for certain dualities. I did not ask regarding a non-perturbative definiton. I did not ask for the n-loop measure for the superstring amplitude.

I asked purely physical questions which are to a large extend independend from these internal technical details. Whether SUSY exists (unkroken at a certain energy) can be decided experimentally, so we expect the theory to be able to make reasonable predictions. Whether a certain particle has a specific mass can be determined experimentally, so again the theory shall be able to make such predictions; etc. etc.

These questions may be too complicated; it may be too early to ask these questions; maybe string theory is not (not yet, never, ...) able to answer these questions (uniquely), but they are certainly not "not well posed".

In QCD it was (over decades - and still is?) a riddle what exactly causes confinement and how one can determine the spin structure of the nucleon. In condensed matter physics as of today nobody is able to tell us the detailed mechanics responsible for high-temperature superconductivity. But these questions are certainly well-posed physically. They are just hard to answer.

 

[tom.stoer]

Again I would like to come back to my (reduced) list of questions

• Are there predictions subject to (accessable to) experimental verification / falsification both in principle and in practice? Are there physical phenoma which (once observed) would kill string theory? My (preliminary) answer based on our discussion is "not yet".
• Are there predictions specific for the string theory context (nothing that may follow from SUSY as SUSY could be true even w/o string theory) Again my (preliminary) answer based on our discussion is "not yet".
• What are the short-term / long-term research programs? Not discussed so far.
• What are the major obstacles inherent to string theory preventing the theory from delivering on its promises? Besides some technical details (omitted fortunately) the main issues seem to be that string theory is still in an early stage of development, that a unique framework has not yet been established, and that therefore physical predictions are still out of reach
• What will be the final theory in terms of strings - a theory, or a framework to create theories? Not yet discussed, but my (preliminary) answer based on our discussion is "more a framework than a single theory".

 

[negru]

I think I agree with suprised on this one. It seems implausible that the "theory of everything" will have a unique solution. But that doesn't mean that no predictions will ever be possible. For example, maybe we'll have a two parameter solution space. If fixing these two numbers leads to different values of the SM constants, the CC, etc., we would still technically have a landscape with anthropic selection, but it would be an impressive achievement nevertheless. So I don't see what the big fuss is about the landscape issue. We could still find some principle able to reduce the solution space enough.


About the specific list of questions.
My answer would be "too early to know" for most of them. To the first two, you should include the ads/cft part as well. If you can compute something on the cft side and it doesn't match, you've just falsified ads/cft. Also, there are objects on the cft side which are only explained by strings (some of them even by classical strings, so nothing fancy at all). This is as specific as you can get.

Short/long term goals? Well there is extending ads/cft, exploring the landscape issue, finding string solutions in various backgrounds, understanding what the M in M theory stands for... All open problems are being worked on as we speak. A really short term (and doable, yet indirect) goal in my oppinon should be just understanding N=4 SYM. There is just so much weird stuff there, with the dualities, the twistors, the wilson loops (stuff that eg arkani-hamed, maldacena and bern have been working on recently). All of this will mean something for string theory in the end.

 

[tom.stoer]

I think I agree with suprised on this one. It seems implausible that the "theory of everything" will have a unique solution.

Where did you get the "unique solution" from?

About the specific list of questions.
My answer would be "too early to know" for most of them.

OK, fits to my impression.

To the first two, you should include the ads/cft part as well. If you can compute something on the cft side and it doesn't match, you've just falsified ads/cft.

Do you mean some generalized gauge/gravity duality? As we said AdS is unphysical / not realized in nature.

 

[negru]

Do you mean some generalized gauge/gravity duality? As we said AdS is unphysical / not realized in nature.

Like I said, no one said ads needs to exist for that to work. If we find a dS/cft duality or something I don't think the dS will be our universe. In the current formulation, you can think of the AdS space as the Hilbert space of QM. Plus, you only need AdS at the boundary. The bulk can be anything.

Or picture this. Say we extend the gauge/string duality to QCD, and it turns out to be C^2/QCD. Where C stands for camel. If we can predict stuff with it, what would that mean for the camel? Nothing, because in this case, the camel is just part of some internal machinery, which relates to the real world only through this particular formalism. It's an abstract camel.

Of course this depends on what you're trying to compute. If you want to compute a real world black hole entropy using the CFT, then yes AdS might not be suitable. If you want to compute gluon scattering amplitudes, it doesn't matter whether it's AdS space or camel^2 space. That's why some of the questions in this thread are not well-posed. You really need to be specific: at this moment, there are various string applications. The exact "physical" features of each of them might be different. You should refer to each specifically so we know what you're talking about.

As a futher example on the issue of ill defined questions. Consider the string/M theory duality. These two live in a different number of dimensions, but they are completely equivalent. So, wouldn't the question "just how many dimensions are there?", be pretty silly? Although it sounds very sensible and "physical", it just doesn't make sense. It depends very much on technical issues.

 

[tom.stoer]

As I said; I understand, but I prefer to talk about generalized gauge/gravity duality instead of AdS/CFT.

I think I agree with suprised on this one. It seems implausible that the "theory of everything" will have a unique solution.

Again my question: where did you get the "unique solution" from? I was talking about a "unique framework"; that means a mathematically well-defined set of axioms / rules / principles / theorems / equations serving as the basis of the theory.

As a futher example on the issue of ill defined questions. Consider the string/M theory duality. These two live in a different number of dimensions, but they are completely equivalent. So, wouldn't the question "just how many dimensions are there?", be pretty silly? Although it sounds very sensible and "physical", it just doesn't make sense. It depends very much on technical issues.

As I said before: this is exactly the kind of technical details of string theory internal issues I explicitly excluded when talking about physical questions (I did not exclude ordinary 3+1 dim. spacetime as this is something we observe).

Anyway: I would hesitate to insist on complete equivalence of two theories which are not yet defined (as we discussed above); or where the "definiton" is restricted to certain approximations.

Or let's turn it round: What is the definition of string and M-theory?

Btw.: similar questions have been asked by David Gross several times:

http://strings2009.roma2.infn.it/talks/Gross_Strings09.pdf, slide #16
http://www.ift.uam.es/strings07/040_scientific07_contents/transparences/gross.pdf , slide#22

WHAT IS STRING THEORY?
This is a strange question since we clearly know what string theory is to the extent that we can construct the theory and calculate some of its properties. However our construction of the theory has proceeded in an ad hoc fashion, often producing, for apparently mysterious reasons, structures that appear miraculous. It is evident that we are far from fully understanding the deep symmetries and physical principles that must underlie these theories. It is hoped that the recent efforts to construct covariant second quantized string field theories will shed light on this crucial question.

We still do not understand what string theory is.
We do not have a formulation of the dynamical principle behind ST. All we have is a vast array of dual formulations, most of which are defined by methods for constructing consistent semiclassical (perturbative) expansions about a given background (classical solution).

What is the fundamental formulation of string theory?

WHAT IS MISSING ?
Perhaps “String theory” is like quantum field theory - a framework and not a definitive theory.
Perhaps we are missing a fundamentally new principle of symmetry, of dynamics, of consistency, ... that leads to a unique solution --- not a “vacuum” but a space-time, a cosmology.
Emergent Space-Time

 

[atyy]

"Experimental discovery of Supersymmetry would certainly give string theory a big boost, and learning how Supersymmetry is broken might very well give string theorists crucial clues about how to proceed." http://conferences.fnal.gov/lp2003/program/papers/witten.pdf

Five Problems in Quantum Gravity
http://arxiv.org/abs/0906.1313

 

[negru]

Ok, unique framework. This definitely. There's just no chance you can have both a "holographic" type framework, and the "traditional" type, both with strings, with absolutely no connection between them. But if it turns out you can, then I'd have to conclude that strings are the most natural language humanity has found so far. I would advocate reinterpreting pythogoras's theorem in terms of string theory if that happens.

My comment about the unique solution was related to the landscape issue, which most string critics are focusing on and which I find completely irrelevant at this stage of development.

 

[Haelfix]

Ben mentioned it in this thread, but the landscape problem of quantum gravity (really high energy physics) is not going to go away and will be a generic problem for any approach, even if they haven't studied or appreciated it yet.

String theory does better than any other current alternative on the market in this regard since it restricts what can come out of the low energy physics (the swampland).

Whereas a high energy theory of gravity that can arbitrarily couple any matter without constraints, will automatically have an (infinitely) worse landscape problem.

 

[marcus]

Whereas a high energy theory of gravity that can arbitrarily couple any matter without constraints, will automatically have an (infinitely) worse landscape problem.

Haelfix, I have often found statements similar to this to be unreliable/misleading and I suspect the reason may be as follows:
They depend on a particular person's necessarily limited individual way of imagining future research.
You could have a very specific format in mind for "coupling matter without constraints" so that what you are saying actually has necessarily limited applicability. Another reader might not realize this and might think that what you are saying actually applies broadly to all theoretical approaches to gravity and matter.
As a check you might want to consider the following hypothetical example and explain why you think it would automatically lead to an infinitely worse landscape problem, if it should happen to work.

You probably know something of Caltech prof. Matilda Marcolli (co-author with Alain Connes on several occasions). Marcolli et al posted this in May 2010. See especially section 8 "Spin foams with matter"
https://www.physicsforums.com/showthread.php?t=402234

If you wish, you could explain why an infinitely worse landscape problem would necessarily arise over in that thread. That way it would not distract from this thread's focus on string theory.

The title of the paper is Spin Foams and Noncommutative Geometry http://arxiv.org/abs/1005.1057

 

[marcus]

I guess what worries me is two things. One is the presumption and tone of omniscience. You present yourself as someone who can imagine every approach to quantum gravity and matter and who is able to foresee a landscape for every possible approach.

... the landscape problem of quantum gravity (really high energy physics) is not going to go away and will be a generic problem for any approach, even if they haven't studied or appreciated it yet...

The other worrisome thing is that this claim seems to be motivated as a defense of string.
The defensiveness is disappointing. You seem to be trying to deflect comment on the string landscape difficulty by the questionable suggestion that all other possible approaches would inevitably suffer the same or worse. It sounds suspiciously like part of some rhetorical battle you think you are engaged in, rather than an objective scientific observation.

 

[negru]

Well, part of the issue is that string theory IS already a theory of quantum gravity. The problem so far is that we cannot determine all the parameters uniquely. Other than that it's pretty ok. Suppose the compactification which leads to the dreaded landscape is shown to contain the SM (and some solution exists with the right constants). Then the problem is that whatever other theory you find (with say a unique solution), would itself just be a particular solution to the more general string theory.
To see if the theories are actually incompatible you'd need to go to higher energy and make a prediction there. This higher energy would likely be around the Planck scale, so good luck with that.

[this is of course assuming that no further progress is made in string theory, in terms of sub-planckian predictions]

So this problem will remain whatever other theories we find.

 

[marcus]

Well, part of the issue is that string theory IS already a theory of quantum gravity...

With all cordial respect, Negru, that is not the issue at all.
I am objecting to Haelfix's unsupported assertion that any QG+M approach which might possibly be invented must encounter a landscape dilemma similar to string's, or worse.

We cannot be sure that what you call "string theory" is the final and only theory of gravity, so we cannot infer that any theory of gravity must encounter the same sorts of problems, as you seem to be suggesting.

What I would like to see Haelfix try to explain concerns the example of Marcolli's joining Spinfoam and Noncommutative Geometry (SF+NCG). That is an approach. (Not an approach I especially favor or know a lot about, but one I've followed over the past 3 or 4 years as it gradually got started.) As an example, I want some plausible argument why THAT approach, just to be specific, must encounter a landscape dilemma.

Haelfix may just wish to retract the broad claim he made and say something more narrowly constructed. Which would be fine! I, for one, would certainly be interested in some revised form of the idea.
Besides Marcolli, there are further possible examples/test cases that one could consider.

If he decides to tackle Marcolli's idea, then I hope he goes over to the Marcolli thread to do it, so it won't distract here. I think the focus here should be on string. And forget about trying to point out presumed flaws with other approaches as a defense mechanism. I gave the link to the Marcolli thread earlier---https://www.physicsforums.com/showthread.php?t=402234

 

[tom.stoer]

OK, I think it's time to focus on the unique mathematical framework.

I guess we agree that old-fashioned string theory + 11 dim. SUGRA is not unique in that sense. It requires different formulations depending on the energy / strong-weak regime.

If you look at QCD there are some low-energy effective theories which are just that (and which cannot be derived but only motivated from high-energy QCD); nobody would doubt that even in the low-energy domain QCD (quarks, gluons) are the fundamental degrees of freedom, even if it's hard to calculate photo-pion production w/o chiral perturbation theory.
Not so in string theory. It is required to change the description once you move to a different regime. It is not just that the calculations are hard if you don't, It seems impossible not to do so. One central issue is that dualities between these different theories are not always established rigorously but only in certain approximations (s-duality). I would accept a framework as unique even if you have different calculational tools in different regimes once you have defined the theory in one regime and once you have shown the equivalence between the two regimes.
It's simpler in QCD as you do not need to derive a low-energy effective theory rigorously as soon as you a) can plug in the phenomenologically correct (experimentally well-known) degrees of freedom which you already know and b) derive some experimentally testable results. As b) is missing in most regimes of string theory one has to go the hard way and stick to more rigorous math.

The discussion regarding AdS/CFT, twistor strings etc. shows that it may be necessary to find new formulations to answer new questions. Still no reliable unique framework exists from which you can always start (again: compare it to QCD).

Let me comment on a few ideas, research programs etc.:

String perturbation theory is not defined beyond 2 loops (3, 4 loops?). Some time ago I studied a paper in which they tried to define the genus 3 and 4 superspace measure. I don't know if this has been achieved; but it is clear that a consistent definition of string perturbation theory including proof of finiteness order by order and convergence of the whole perturbation series is still not available.

Then what is non-perturbative string theory? Or what are quantum mechanical completions of effective solutions / vacua? In most cases one throws away all the high-energy string modes and uses the low-energy effective theory, e.g. MSSM-like models. As this is fine from the phenomenological point of view it is not useful in defining the theory. It can serve only as a specific expansion aroung a specific vacuum ( as an example: it cannot describe picking one vacuum neither tunneling between vacua).

I haven't seen much about second quantized string field theory. Could this be one unique framework with descents to other more specific formulations?

Regarding M-theory: What is the current state regarding infinite-dimensional matrix theories, emergent gravity and/or tri-linear algebras? Of course this is work in progress but are these really candidates to define the theory uniquely? to identify the "fundamental" degrees of freedom?

Is there a framework available in which fully dynamical spacetime (beyond the pertubative graviton limit) can be studied? (this is related with the usual question regarding background independence). Afaik this is more or less settled as soon as a framework regarding gauge/gravity is available. But as we saw this is realized only in certain specific cases like AdS/CFT. Would the uniqueness issue go away once one can establish such a duality, being able to translate all questions regarding fully dynamical spacetime into more tractable field theory stuff?

Again let me conclude with David Gross:

WHAT IS STRING THEORY?
This is a strange question since we clearly know what string theory is to the extent that we can construct the theory and calculate some of its properties. However our construction of the theory has proceeded in an ad hoc fashion, often producing, for apparently mysterious reasons, structures that appear miraculous. It is evident that we are far from fully understanding the deep symmetries and physical principles that must underlie these theories.

 

[tom.stoer]

@marcus, Haelfix: the discussion you started is certainly interesting, but why should we care about a landscape problem in theories X, Y, Z, ... if we know that they are not related to strings - but strings are the unique theory (including gravity)?

My guess is that what we call landscape problem is due to the fact that we have one great achievement in string theory, namely that it turned theories into solutions / vacua. That is nice, but it does not make all the theories go away. There seems to be not so much difference whether there is a landscape of theories or a landscape of vacua :-)

 

[suprised]

That is nice, but it does not make all the theories go away. There seems to be not so much difference whether there is a landscape of theories or a landscape of vacua :-)

Yes indeed, however some people like Tom Banks have an interesting take on that, see his recent TASI lectures.

But I should clarify some aspects that are often confused/deliberately misrepresented, concerning landscape, predicitibilty and so on. It has been often stated that string is "unique", on the other hand critics claim it makes "no predictions" - as if string theory would be a completely structureless, floppy, ambiguous, ad hoc mathematical construct which leads to arbitrary results.

The point is of course, as has been said before, that a unique theory can have arbitrarily many solutions (like electromagnetism that governs all possible DNA molecules for example), which is a fact probably understood by anybody.

But what is often overlooked, is that once a solution is chosen, ie. a background around which to expand, there are infinitely many scattering processes one can do, in principle, which leads to infinitely many predictions. That is, string theory is quite the opposite of a random arbitrary theory, rather the infinite mass spectrum and all the interactions between these infinitely many states are finely tuned and completely determined, __once the background has been fixed__. In other words, there are infinitely many counter terms in the effective field theory that arise from integrating out the massive spectrum around a given background, and in principle each one could be tested by scattering experiments and so this leads to infinitely many "predictions". And if just a single one of such terms would come out wrong experimentaly, or one predicted massive state would be missing, this would disprove string theory; as the missing of any single state, say at the one millionth mass level, would render the string theory immediately inconsistent.

I am not claiming, though, that we humans of today would be able to do such computations, nor do the experiments, rather this is a matter of principle. This is to illustrate that string theory is an exceedingly determined theory without any room to adjust -- except for the ground state (it seems). The unfortunate thing is that we humans with our limited capabilities are able are able to access only the physics of the ground state and not the excited string spectrum; but in a sense this is our own fault and not the one of the theory ;-)

Things may however need not be as bad, as there is the (remote) possibility that the string scale is very low after all, and if it is near the weak scale then one might be able to see massive string states and KK states even at the LHC. There are a some papers out analyzing this situation, including plots of cross sections, so very clearly string theory can make specific predictions; even if measuring a finite number of such resonances would not logically prove that the theory is right (as the one-millionth might be missing, eg), it nevertheless would amount to a physicists’ proof of string theory (well, the armcair critics would never accept this that but who cares?)

I hasten to add, though, that finding such a scenario is extremely unlikely, as there is no real reason why the string scale should be so low. We certainly expect that “something” must happen at the weak scale, and finding susy or extra dimensions or string states are just less or more remote possibilites/wishful thinking.

Finally some remarks on predictibility; so far we talked about massive states and counter terms in the effective action at low energies; what about predicting the structure of the standard model, eg.? Indeed IMHO there is no way that this can be predicted from string theory as of today. It always amounts to make certain choices, eg about a brane configurations, fluxes, manifolds, etc, and one could make other choices as well. This is not a specific failure of string theory, but of any other theory I know - let’s mention Connes’ setup (or Lisi’s construct, which I wouldn’t call a theory); in each case one makes some choice (eg of the non-commutative geometry, the gauge group, the space-time dimension, etc), and then one goes from there. This is morally the same “problem” that string theory has, and there is no answer why just this structure is chosen as compared to any other possible one. In string theory, those ad hoc choices are interpreted as choices of background, in other theories these choices just define the theory. I would view the situation from the string point of view, namely as solutions of one single theory, as more satisfying, though in practice it doesn’t make much of a difference - this relates to the first line and is a good place to stop for now!

 

[tom.stoer]

surprised!

Thanks for the long and well-elaborated statement. In the light of our discussion I agree with most of your ideas (except for minor details which I don't want to discuss - just to stay focussed). As I already indicated: accepting that string theory's major achievement is to turn fundamental (gauge) theories into low-energy effective theories or ground states goes hand in hand with accepting some kind of landscape.

Of course I expect that there will be additional discoveries restricting possible vacua, telling us more about dynamical selection principles, stability, tunneling, etc. This will perhaps reduce the number of vacua, lift some degeneracies, ... but in the end we will still face a reduced landscape (unless a third superstring revolution will throw over everything).

I do not agree with haelfix that all theories will face a landscape issue b/c nobody knows all theories - not even within string theory, let alone other theories like LQG, NCG or XYZ

But again this brings us back to Gross' question and to my last two topics (slightly adjusted)

• what string theory really is
• what the final theory will look like (in terms of strings or other fundamental degrees of freedom?)
• what the major obstacles (inherent to string theory) are preventing us from constructing this unique mathematical framework

Anybody out there who wants to comment on these questions?

 

[Haelfix]

Another reader might not realize this and might think that what you are saying actually applies broadly to all theoretical approaches to gravity and matter.

I would hope that a reader would realize that what I am saying is that in fact it DOES apply broadly to any tentative theory of matter.

What we now know, which wasn't necessarily appreciated a few years ago, is that a landscape of meta stable vacua is not just a truism about KKLT in string theory, but also a *generic* property of quantum field theory (and not just supersymmetric ones) including the standard model.

That is to say, any theory (under a reasonable set of conditions like having a reasonable scalar spectrum) that wishes to include gravity, and that contains a small cosmological constant and that possesses the standard model as an effective field theory at low energies also necessarily has a large landscape of metastable vacua.

Nima, Michael Dine and a few others have convincingly shown this, and I emphasize again that it is completely independant of the nature or properties of any tentative UV completion at high energies.

See for instance arXiv:hep-th/0703067

 

[suprised]

[*]what string theory really is

A quick provocative claim: what we have constructed so far is nothing but a portion of the space of the consistent theories that include gravity.
(This could be refuted by presenting a theory that is consistent but is not contained in this framework; in a sense this is the question whether the "swampland is hospitable" or not.)

If it is just that, then what we call "string" theory (including 11dim M-Theory that is not a string theory) is a framework that is useful to describe/parametrize this space of consistent theories, in certain regimes at least. But which does not out of itself determine the ground state etc.

I would view this analogous to gauge theory. Much like N=4 supersymmetric Yang-Mills theory is an interesting model for real world QCD (with important differences and simplifications), the ten dimensional string theories and their compactications with many supersymmetries are models for gravitational theories. They are useful for studying certain aspects like non-perturbative phyisics and black holes. But in the same spirit in which one should not view N=4 gauge theory as being underlying (or more fundamental than) QCD, one should not view those string theories as underlying the real world.

 

[mitchell porter]

Anybody out there who wants to comment on these questions?

At any time, there are dozens of papers proposing to be the next big thing, saying we need to think about "BPS preons", or "Azumaya noncommutative geometry" of D-branes, or "representation theory of higher categories of cobordisms", or E_n with n>8... But I'm still learning the basic duality web of the mid-1990s, so I certainly can't tell you if any or all of these is relevant to the future. I can only mention a few statements I've gleaned from the literature.

(1) The string coupling can vary dynamically. But in M-theory, the 11-dimensional corner of the duality web, this quantity turns into a new spatial dimension, so you can't take strong or weak coupling limits of M-theory proper. This has something to do with the difficulty of writing down an equation for M-theory. Ashoke Sen and others say that M-theory won't be understood until the whole theory is understood. But we could still turn this around and say that understanding the M-theory corner should help us understand the whole theory. The tri-algebras you mention provided incremental progress here because they give the worldvolume theory for a stack of M2-branes.

(2) I believe you need a different matrix model for each distinct spacetime background. (There is more about this in Lubos Motl's thesis.) So matrix models, while important, aren't The Answer.

(3) String field theory also isn't The Answer. Edward Witten, who invented it, long ago dismissed it as "too messy" to be fundamental. The one important role it played in recent times, that I know about, is Sen's work on tachyon condensation and brane-antibrane annihilation. The tachyon is usually unwanted because it has negative energy. But here it just balances out the positive energy of the brane tensions.

 

[tom.stoer]

A quick provocative claim: what we have constructed so far is nothing but a portion of the space of the consistent theories that include gravity.

If it is just that, then what we call "string" theory (including 11dim M-Theory that is not a string theory) is a framework that is useful to describe/parametrize this space of consistent theories, in certain regimes at least. But which does not out of itself determine the ground state etc.

As I said: forget about the ground state, I can live with the landscape, but I (and Gross :-)still miss a well-defined mathematical framework and underlying physical principles.

So the provocative question of Gross does not mean what string theory currently is - here I agree with your claim - but what string theory fundamentally is? (compare it to the situation in the early days of quantum mechanics).

 

[tom.stoer]

Hello Mitchell,

thanks for your ideas. My conclusion is that M-theory seems to be nothing else but a new domain of the full space of theories with its own mathematical framework, technicalities and their specific limitations.

So it's not the mother-theory :-)

But in the very end we are all expecting one unique defining equation, one mother of all theories, don't we?

I do not know who had the idea here in the beyond-forum; it goes like that: think about a huge complicated n-dim. manifold for which you need a huge number of coordinate charts. You have to construct each chart and each mapping between two overlapping charts seperately. Whenever one inspects a new region of the manifold one finds new topological structures, new coordinates, new maps etc. There is no global view! Now compare this to string- / M-theory: perhaps all the different pieces (theories) we have so far are nothing else but these different charts, the dualities are the maps between the theories. Once we investigate a new domain of string- / M-theory we eventually find new structures, new dualities etc. So again there is no global view for this manifold or space of theories (and therefore no single defining equation).

Is it just that? Or is there anything around the corner - a third superstring revolution - which harmonizes all these theories into a single defining framework from which they can be derived - at least in principle?

 

[suprised]

I do not know who had the idea here in the beyond-forum; it goes like that: think about a huge complicated n-dim. manifold for which you need a huge number of coordinate charts. You have to construct each chart and each mapping between two overlapping charts seperately. Whenever one inspects a new region of the manifold one finds new topological structures, new coordinates, new maps etc. There is no global view! Now compare this to string- / M-theory: perhaps all the different pieces (theories) we have so far are nothing else but these different charts, the dualities are the maps between the theories. Once we investigate a new domain of string- / M-theory we eventually find new structures, new dualities etc. So again there is no global view for this manifold or space of theories (and therefore no single defining equation).

It was me, see: https://www.physicsforums.com/showpost.php?p=2386391&postcount=9
This expresses my personal view, and the view of other colleagues but certainly not of all of them. And I am very glad that at least one can remember a statement over threads.

 

[tom.stoer]

Not all statements are worth to be remembered :-)

 

[atyy]

In fact, Haelfix's claim is self-evidently correct.

 

[tom.stoer]

In fact, Haelfix's claim is self-evidently correct.

which one? regarding the landscape issue?

 

[atyy]

which one? regarding the landscape issue?

Yes, the one about a theory of gravity which can couple to any form of matter.

 

[tom.stoer]

I don't care in this context. We have a candidate theory (string theory) which has the landscape problem. Regardless if it's right or wrong, it is obvious that nobody will find a new candidate theory w/o any connection to strings but as deeply investigated as strings within the next couple of weeks. But as soon as this new theory is published (I am checking arxiv daily), I will open a new thread.

 

[BenTheMan]

I guess what worries me is two things. One is the presumption and tone of omniscience. You present yourself as someone who can imagine every approach to quantum gravity and matter and who is able to foresee a landscape for every possible approach.

It's very possible that some, as of yet uninvented, approach to quantum gravity may evade these problems. Of course, the burden of proof is on that community to actually come up with a workable theory first. Surely it is possible that such a theory exists, but it is also possible that the LHC will produce fire-breathing dragons which will ravage Europe. It's also possible that some bright graduate student will find a selection principle on the landscape and predict the electron's mass from string theory. It's just not likely.

The point is, you have to follow your nose. When you build a model or a theory, you have to first start with what has worked for you in the past, and then build from there. And at every stage you have to make sure that you effective field theory matches the standard model or the MSSM.

So Haelfix's comment is right, given what we currently know about the theory of quantum gravity, based on 100 years of research of some very smart people. Is it possible that 4 generations of work has led to the wrong conclusions? Sure---it's happened before.

So you can wring your hands and say ``We just don't KNOW!'', or you can shut up and calculate something, and try to advance the state of knowledge to the best of your abilities. Naval gazing works for some, but not for people who are interested in science.

 

[BenTheMan]

A quick provocative claim: what we have constructed so far is nothing but a portion of the space of the consistent theories that include gravity.
(This could be refuted by presenting a theory that is consistent but is not contained in this framework; in a sense this is the question whether the "swampland is hospitable" or not.)

See Wati Taylor's recent work regarding the swampland in 10 and 6 dimensions.

 

[MTd2]

So Haelfix's comment is right, given what we currently know about the theory of quantum gravity, based on 100 years of research of some very smart people.

What is *the* theory of quantum gravity?

Are you single?

 

[marcus]

In fact, Haelfix's claim is self-evidently correct.

https://www.physicsforums.com/showthread.php?p=2826555#post2826555

 

[petergreat]

Regardless if it's right or wrong, it is obvious that nobody will find a new candidate theory w/o any connection to strings but as deeply investigated as strings within the next couple of weeks. But as soon as this new theory is published (I am checking arxiv daily), I will open a new thread.

In the 19th century, no amount of ingenuity from theorists could've explained Mendeleev's periodic table before J J Thompson actually discovered the electron and before the development of quantum mechanics! The SM is better than the periodic table but still has 20+ free parameters. After so many years of efforts in vain, is there any reason for believing that such an absolute mess can be explained from theory alone, without some revolutionary experimental discovery? I don't believe yet another speculative theory posted to arxiv (which will reach you on the same day) will magically solve the world.

P.S. Maybe people should simply give up before seeing new experimental hints?