Why I am REALLY disappointed about string theory

[tom.stoer]

Just to point out the first that comes to mind, string theory contains gravity while it remains to be shown that so does LQG.

What about LQC which has FRW cosmology as a limiting case? What about deriving graviton propagators from spin foam? Of course not everything is completed in LQG, but afaik there is no fully developed string theory on dynamical backgrounds, either; so both programs are work in progress.

But this is not relevant here. I don't think we should compare LQG and string theory in this thread (we can do that, but not here, as we would immediately start to argue about LQG; this is a different subject). I started and continued this thread w/o mentioning LQG (hopefully :-), simply to avoid this never-ending discussion from the very beginning.

 

[atyy]

Please let us know according to which standards you measure being ''ahead''?

And which achievements show clearly enough that strings are way ahead of LQG?

Just a quick answer and I'll refrain after this, since following tom.stoer's note we shouldn't get into this discussion here.

From my lay point of view, strings are ahead becasue
1) Strings have gravity.
2) The AdS/CFT correspondence is a non-perturbative formulation of quantum gravity in some universes, and a concrete example of the emergence of space

LQG has not been shown to contain gravity. The theory is not well-defined ( http://arxiv.org/abs/1010.1939 , Eq 26). The "classical limit" addresses only kinematics, not dynamics ( http://arxiv.org/abs/1101.5061 ). My interest in LQG is that since string theory has shown that theories without gravity can contain gravity, maybe the LQG formalism does contain gravity, if it is interpreted differently.

 

[atyy]

Haha, as a place to start, I would be willing to bet US $100 that no string construction will predict the electron's mass in the next 20 years. By predict I mean roughly the following: we may find a vacuum that has the electron's mass right (that wouldn't surprise me), but string theory should have given some reason why this vacuum should be preferred to any other. Or perhaps shown how the vacuum/landscape language I'm using is misleading.

I'm a reasonable monkey physicist , I would be happy to pay up if anything remotely predictive came out of string theory (regarding high energy particle physics).

A tangent: I think condensed matter folks have long wanted a landscape (eg. Wen's manifesto at the start of his QFT text, if I'm reading it right). So from that point of view, the landscape is an achievement of strings?

Edit: I wrote the above before seeing these:

For example, suppose you have a vacuum that closely resembles our world.
1) I would imagine that there are hundreds more with slightly different low energy parameters.
2) And similarly, I would imagine that there are hundreds with the same low energy physics but with varying physics at higher energies.

1) is very familiar from condensed matter physics where we often have continuously variable parameters.
2) is an example of low energy universality i.e. the relative independence of low energy physics from the high energy details.

Holographic duality tells us that this intuition also applies to some part of the string landscape.

Another example from condensed matter physics. Suppose you were a tiny organism living inside a material in one of the labs down the hall. You discover through a series of ingenious high energy experiments your proposed theory of everything: electrons hopping on a lattice interacting electrostatically. You look for symmetry principles telling you that the lattice you found is the perfect lattice, that it had to be that way (haha, that actually sounds a lot like string theory). You write a popsci book declaring that you will soon compute all the interesting constants of nature: the speed of phonons, the mass of low energy quasiparticles, etc. But then you discover that far from giving a unique answer, the high energy theory predicts all kinds of worlds you've never seen: different lattices, different phonon speeds, different critical temperatures for the various phase transitions you've observed, different phases you've never seen. And you finally realize that knowing the high energy theory doesn't ultimately tell you that much about your low energy world. But that's ok because the high energy theory is still interesting and useful and it opens your eyes to wonderful new possibilities. That is what I understand string therory to be.

As long as the number of parameters needed to describe the vacuum is less than the current number of parameters in the Standard Model, it's more than enough. There's nothing bad about having a landscape. In my opinion, like in yours, having a landscape of solutions is the most sensible thing a theory of everything can have. We shouldn't we be able to have a theory in which the electron mass is not X, but X+0.0000000001 ? Like there is no sensible reason why the Earth's mass is X, but there is nevertheless a mechanism which can explain how it got that mass.

 

[qsa]

The reason why you can have a landscape problem in string(or any other similar in nature) is that the model is not designed from a fundamental entity. it is designed with a make blieve properties,just like point particles carrying charge, spinning(we don't know how) , has a mass! , it's a field and a particle and the list goes on and on. We do that by playing the diff equation game, the price you pay is that now you can twist things all the hell and create parameters and play with them as you please. These models are inherently free for all.

As a matter of fact if the universe is designed from a funamental entity, it will become clear that no much freedom exists in designing the universe. So, this entity is unique and whatever relations among these entities will be bounded, and that is how you get a finite orderly universe that is comprehensible. Sorry, Einstein.


.

 

[negru]

I agree that if we can't search the landscape it won't be very useful. But yeah, otherwise to me it's a good thing to have one. Having a unique solution might have generated nobel prizes more quickly, but I wouldn't have found that option more satisfying than our current predicament. There's no obvious reason why the parameters should have the unique values they have. We'd just like them to have specific values to test out theories - but what we want or need says nothing about how things actually work.

 

[tom.stoer]

I agree that transforming a landscape of theories into a landscape of solutions is a big success of string theory. But there are several problems:

1) up to know you do not have a unique theory from which you can derive one landscape and its vacua; instead you have different approximate theories (related via exact or approximate) dualities which by themeselves define a (small) landscape of theories
2) up to now you are not able to calculate (not even approximately) any of the physical parameters we are interested in; you cannot derive the low-energy mass spectrum and the coupling constants in the (nearly realistic) vacua
3) once a set of vacua is known, there should also be some selection principles forcing the theory to adopt some vacuum states

In condensed matter physics there is one single theory (1) from which - via certain approximations - one can derive effective theories describing condensed matter states. One is able to calculate (approximately) certain physical parameters like density, heat capacity, ...(2). And one is able to specify certain conditions (temperature, pressure, ...) that force the system under consideration to be in a specific state (liquid, magnetized, ...) or show certain excitations or effective degrees of freedom (phonons, polarons, ...). In string theory the unique theory is not known, the calculations are not possible, the effective degrees of freedom are partially known but the selction of specific vacua, the transition between vacua etc. are not known.

 

[negru]

Yes I completely agree, and I also agree with the ordering of your points. We should first understand what the unique framework would be, if there is one, or what else dualities can teach us, before we even attempt to ask whether a selection principle exists.

Which is why I'd personally consider any work on selection principles or computing parameters to be way premature, and likely a waste of time. And this is why we still need to focus on more subtle issues, as well as ads/cft. Again it is my opinion that we won't find out too much from strings before fully understanding ads/cft - which is why many string theorists are working SYM for the moment. This however is something that most critics will complain about.

 

[tom.stoer]

Yes I completely agree, and I also agree with the ordering of your points. We should first understand what the unique framework would be, if there is one, or what else dualities can teach us, before we even attempt to ask whether a selection principle exists.

Thanks. This is one of the posts which distribute the disappointment I felt when starting the whole discussion.

 

[Fra]

We'd just like them to have specific values to test out theories - but what we want or need says nothing about how things actually work.

What I tried to convey is that AFAIC if you attempt something as bold as a theory of theories, then you are doing inference. It's more than just physics, and with this I don't mean it's mathematics, I mean it's a general theory of rational learning to describe any scientific process. And in this perspective the theory is an interaction tool for learning and interactions.

Here, how things "actually work" refers to how inference works, not how an electron behaves.

(although with a separate conjecture, that I personally make, you can make this even more radical by thinking that any physical interaction IS an inference. In this perspective, it is not the case that our inference says nothing about how things "actually work". The very radical point here is that it does)

I've expressed this view before, but my point is that if you take ST to really by the grand thing that at least some people think of; like the theory of theories... in a deeper sense. Then one must also take the inferencial perspective serious, or it simply doesn't stick together.

For me, this "vision" of ST as theory of theories, is not bad at all, it's just that it was NOT how string theory was started. I think it's at best something that may be some conclusion from failing to find a unique theory. But still, most arguments I have read from string people, does not seem to acknowledge these points.

In short, there is a lack of understanding what the landscape really means in terms of inference. That's my firm opinon. Paradoxally, string theory may hint this, and some other camps critique it, but it seems that string theory isn't the right "theory of theory", becuase some basic traits are missing.

Fill in those gaps, and I would be prepared to take it more seriously as an inferencial theory.

/Fredrik

 

[Fra]

1) up to know you do not have a unique theory from which you can derive one landscape and its vacua; instead you have different approximate theories (related via exact or approximate) dualities which by themeselves define a (small) landscape of theories

I have to admit that from my perspective, I do not think the lack of a unique meta theory of theories is a problem because I don't see how such a meta theory could be inferred as independent of the inference system used to infer it. It just doesn't make sense.

The only way it could be realized is as a conjecture, or element of structural realist reality. But those kind of things is exactly what I think are non-inferencial.

I think the landscape itself must evolve and can only be described from the point of view of an observer; and this evolution can not be predicted by the same observer. But it can be predicted by other observers.

So the landscape of theories defining the first layer of landscapes is then just corresponding to the observers. IMHO the landscape problem should thus related to the population of inference system in nature and is thus perfectly analogous to evolution. But this is not the same as the antrophic principles.

A landscape ~ diversity of inferencial systems

Not all points in the landscape are viable for the same reason we do not find one-legged lions in nature - even though such a lion would be perfectly "consistent". This is why consistency is an insufficient selector here, we need to account also for the fitness.

Unfortunately, i don't see that string theory as it's formulated, starting with the continuum etc, is able to provide the analysis needed to push this to the next level. Too many things needs to be reworked that it probably wouldnt' be string teory anymore except as a limiting inferencial model where the continuum is realized. But I am convinced that the resolution of the problems here lie at the level prior to the continuum.

/Fredrik

 

[Physics Monkey]

This sounds overambitious for now.

Sorry, I didn't understand you. This means that you also think strings won't make a prediction for the electron mass anytime soon?

However, having a landscape doesn't mean one can't make predictions. People who say that really haven't thought about the topic too much or are just playing dumb. It doesn't matter if there are 10^500 solutions, or a continuum of them.

Of course, I agree that just the existence of a landscape does not imply lack of predictivity. However, I also think landscape issues tend to shift thinking, forcing one to ask different types of questions and make different types of predictions.

In fact. the improvement from 23 something parameters to 10^500 different solutions is quite big. The latter has measure zero in the former. It's infinitely better. Calling it a plague is really disingenuous. Assuming that some solutions come close to reality of course.

While I agree in a certain mathematical sense that a finite set is better than a continuum, 10^500 is still far beyond tractable if the landscape is "rugged". And besides, unless I missed something, we do not know that the solution space is discrete just as we have poor control over non-susy vacua. By the way, who calls it a plague?

 

[fzero]

While I agree in a certain mathematical sense that a finite set is better than a continuum, 10^500 is still far beyond tractable if the landscape is "rugged". And besides, unless I missed something, we do not know that the solution space is discrete just as we have poor control over non-susy vacua. By the way, who calls it a plague?

I believe that the argument for a discrete space of solutions is the following. A point in the landscape is particular background where the scalar fields (moduli) have been fixed to their minima in some potential. One way to generate this potential is to add fluxes through compact cycles of the internal geometry of the background. But these fluxes are quantized, so in turn the moduli vevs depend on discrete parameters.

Non-SUSY vacua could be considered (I'm not implying control), but it depends on what question you want to ask and what scale you are working at. Usually one looks for theories with low-energy SUSY and the presence of a suitable Higgs sector. If SUSY is found at the LHC, it would at least confirm that such solutions are the ones to look for. It would be much harder to try to determine a landscape of nonSUSY theories at 1 GeV.

 

[Fra]

I know this thread already arrived at several summarized conclusions from Tom, but due to this last thing I'd like to add one thing that is important for me, but not necessarily for someone who doesn't get the point of lack of uniqe theory.

The logic of the critique against ST can be seen originating from two views.

1. A certain amount of critique can be traced to the understanding that a theory must be unique as to be cleanly falsified. Ie. it's a critique AGAINST the general concept of theory or theory (=framework), and it's lack of unique predictivity.

2. Another crituque, where I belong, is those that arent string theorist, but still appreciate the concept of theory of theory in the inferencial sense. This type fo critique is very different from those jumping on ST failure to confirm to the old style definite theory, and falsification scheme. Instead the argument here is that ST doesn't seem to have all te right properties that seemse necessary from such a framework.

Some evidence of the confusion is that as far as my impression goes from listengin to string theorists, the exact meaning and handling of the landscape in ST is of some debate even within ST - suggesting that this is somthing ST stumbled upon, rather than been constructing principle. The defense of the landscape seems to be of debate.

/Fredrik

 

[tom.stoer]

I am not sure if I get this point. Perhaps there is the problem that it's not so clear what "the landscape" really is and if this ladscape s uniquely defined (I do not mean "defined" in the sense of a complete set of vacua, but in the sense that I can give you a short definition which summarizes all abstract properties of the landscape).

I have the impression that we talk about different "levels" of landscapes.

Looking at one specific string theory X which one can write down in the sense of an action integral one can derive a certain set of vacua (and one can expect other vacua not constructed so far) and call this set of vacua "landscape L[X] of theory X". I am not sure if this definition via "vacua" is exhaustive, because there may be "wrong" vacua, tunneling, etc.

Then there is the meta-landscape ML generated by different theories X, Y, ... where the problem of defining a theory enters the stage. Here I would expect (from a traditional point of view) that one can construct a unique theory (or meta-theory) from which all other theories can be deduced (at least in principle). The starting point is the set {M, SUGRA, I, IIA, IIB, E(8), SO(32)}. I mention M simply as a member of this set as I don't think that M-theory in it's current stage is the unique mother-theory. It's nothing else but a new limiting case of "something". Now looking at the dualities between these theories I still do not see that this set is fixed once an for all. The discovery of M was a kind of surprise and I guess there may be more surpises waiting for us.

Last but not least I am not sure whether the two levels of landscapes L and ML are not intertwined somehow.

Things are rather simply in condensed matter physics. One has QED as a fundamental theory and one can derive a landscape of vacua (ice, iron, ...) with certain effective description (phonons, spin waves, ...). I think there is no "mix of levels of landscapes". I do not have this clear picture in string theory - but perhaps this is simply due to my limited expertise on this subject.

 

[tom.stoer]

Last but not least my feeling is that at a rather early stage there was a wrong turn (I cannot tell exactly which one) which prevents us from asking the right questions. This is our blind spot.

Think about condensed matter physics and classical electrodynamics. You can do a lot based on continuous approximations like electrodynamics in media using polarizability, susceptibility, ...; you can use effective theories like navier-stokes equations; you can study London equations, Ginzburg–Landau theory, ... I would say that collecting those effective theories one can study a huge amount of condensed matter physics. Perhaps one can even use a kind of construction principle, I would say this could be Maxwell plus Schroedinger equations.

Unfortunately based on this construction principle one is not able to ask questions based on photons. They simply do not exist in this framework. So the framework allows us to construct a nearly exhaustive description of low-energy phenomena is therefore certainly "right". But at the same time it's incomplete as it is unable to ask the right questions about photons. Now in this case you have experiments at hand which force you to think about potons (photo-electric effect), but in string theory these experiments are missing. Therefore we must find the correct theory (theories) simply by matehmatics, logics and intuition. No experimental guideline! Even worse we are not even able to say which experiments are missing. We are not ableto ask these questions in the string theory framework.

String theory (as any other theory) limits our ability to ask questions. w/o further experimental input we are stuck. In the standad model we can ask questions regarding the Higgs boson. We can even ask questions regarding alternative mechanisms and we are not stuck once the LHC shows that there is no Higgs boson.

Now the problem is that I can only say that at a very early stage in string theory we may have chosen the wrong direction. From that point onwards we lost the ability to ask questions which would enable us to overcome the blind spot of string theory.

Now let's talk about other theories, like LQG. I don't want to promote LQG as the alternative theory to string theory in sthe sense that it has the ability to achieve unification of forces. I don't think so. I am simply saying that LQG is able to ask different questions. LQG is able to ask questions regarding an algebraic spacetime structure. This question is (afaik) not pronounceable in the language of string theory (maybe I am wrong; I am not an expert on matrix models).

So an alternative theory X may have some value because it enables us to ask different questions. If these questions seem to be "wrong" in the context of string theory this is not a problem of theory X, but a step forward for string theory - provided one accepts that this question could make sense in general and that one should try to find out what prevents string theory from asking this question.

Perhaps there are string theorists here able to tell us what could have been this wrong turn in the very beginning.

 

[atyy]

Think about condensed matter physics and classical electrodynamics. You can do a lot based on continuous approximations like electrodynamics in media using polarizability, susceptibility, ...; you can use effective theories like navier-stokes equations; you can study London equations, Ginzburg–Landau theory, ... I would say that collecting those effective theories one can study a huge amount of condensed matter physics. Perhaps one can even use a kind of construction principle, I would say this could be Maxwell plus Schroedinger equations.

Unfortunately based on this construction principle one is not able to ask questions based on photons.

What about http://arxiv.org/abs/cond-mat/0407140 ?

 

[Haelfix]

Certain very special vacua do allow you to calculate certain low energy quantities exactly. Like for instance the infamous prediction of the top quark mass by stringy methods before it was discovered. This of course was a bit hokey and presumptous at the time, and I think it has been understood that those particular subclasses of vacua are ruled out, but well it illustrates the point.

So for certain classes of vacua, it is often the case that you will have fixed values for certain low energy quantities (or at least ratios or differences thereof), and these won't change upon continuation deformation of the geometry (at least 'quasi locally' in the moduli space). However at the same time, you might have other parameters that have large continuum like spacings. So it might be possible one day to find some appropriate selection mechanism that reduces things down to a subclass where you can specify the electron mass exactly, but need experiment to say figure out what the neutrino masses are (b/c they might take a discretum of values +/- N * .00000000000001 ev where N is an integer).

Yet another case one finds in the phenomenology literature is where you have some vacua that you know in principle gives a unique value for some parameter, but the calculation is so horrendous that you end up having to impose parametrizations by hand anyway!

My personal belief is that I suspect that there is likely myriad selection mechanisms out there (both microscopic and cosmological) and its just a question of time and research before we start finding vacua that are in some sense truly priviledged, and I do think that if any theory has a chance of doing this, it would be string theory (b/c it is so tightly constrained and has such large symmetry and duality groups acting on it).

Moreover, I also think it to be fairly likely that the KKLT like constructions will go away, b/c we haven't entirely understood what's going on with the cosmological constant properly.

That hasn't been talked about much in this thread, and its ashame b/c imo its the single biggest theoretical knock on string theory (or any theory of quantum gravity). Namely the complete lack of a prediction or explanation for this value which on dimensional grounds it ought to be able to predict.

Taken at face value, the existence of a tiny but positive cosmological constant implies several really ridiculous things about the nature of our universe.

1) That we live in a universe that admits finetuning to one part in 10^120, 10^60, or 10^32 depending on how you count or if you admit supersymmetry or not.
2) That we live in a universe that steadily approaches DeSitter asymptotically. Now for various reasons, its likely that asymptotic DS space doesn't exist as a full quantum theory, and so we are reduced to invoking really vague bubble nucleation events to get us out of that embarrasment! Highly unsatisfying I might add.

 

[tom.stoer]

I agree, the cc is a big mistery. In QG there are attemps to predict its low-energy value dynamically based on renormalization group approaches (asymptotic safety). In LQG there are attempts to introduce it kinematically via quantum deformations of the underlying SU(2) which does not fix its value and which does not allow for any "flow". So at first glance both approaches cannot be reasonable at the same time.

Question: why do you think that dS space does not exist as a full quantum theory? (what does that mean exactly?) Is it based on string theoretic reasing, or are there more general ideas?

 

[Fra]

I don't have much time to write a lot atm but I think this kind of discussion is good. Hopefully some of the pro strings may contribute too. I see myself as commenting from my own inferencial perspective only.

My personal belief is that I suspect that there is likely myriad selection mechanisms out there (both microscopic and cosmological) and its just a question of time and research before we start finding vacua that are in some sense truly priviledged, and I do think that if any theory has a chance of doing this, it would be string theory

I think we can distinguish between two kinds of uniqeness here, that are easy to confuse when we are talking about theories of theories.

I do think that human scientists will be able to come to an agreement about the inferencial framework, but this is just to the extent that human based science constitutes a certain class of observers.

I still think it's necessary for understanding unification of interactions exactly how theories as well as frameworks changes with the observer. In this sense two observers/systems interaction can be abstractly seen from the inferencial perspective as an "interaction between two theories". In this interaction both theories excerts selective evolutionary pressure on each other to establish objectivity.

So even though I do think that there will be from the point of view of human science a unique framework (at some level) I think it's a conceptual mistake to think of this as eternally true timeless properties of the universe, which singles out a unique observer independent theory. If one assumes that, it at the same time becomes impossible to understand it. If a theory is an interaction tool, this is always observer dependent. This is why I think there is still plenty of things yet to understand around this.

/Fredrik

 

[A. Neumaier]

Last but not least my feeling is that at a rather early stage there was a wrong turn (I cannot tell exactly which one) which prevents us from asking the right questions. This is our blind spot.

Since you seem to be aware of there being a blind spot, what would be the right questions to ask, from your perspective?

 

[mitchell porter]

Basically, I think its crazy to think that structure of the world at a few GeV tells us much of anything about the structure of the world at $$10^{18}$$ GeV (and vice versa)...
This is because I suspect the landscape is a real thing. Does anyone really think that string theory, with all its incredible richness, can't accommodate a bit heavier of an electron, or an extra generation of very heavy particles, or any number of other minor (or even major) tweaks?

Factually, whether or not it can do this is unknown, for two reasons: we don't know the global structure of string theory, and small nonzero masses are apparently very hard to calculate in string models.

The AdS/CFT duality encourages me to think of string theory as consisting of a large number of separate quantum theories - you could think of them as different superselection sectors - one for each distinct boundary theory. Then you have the work by Brian Greene and others on how the space of CY manifolds is connected by conifold transitions (also see the much more recent work of Rhys Davies on "hyperconifold transitions"), which suggests one big theory. It's very unclear to me how it all comes together in the end. Maybe there are one or two "big" superselection sectors, in which a large number of different CY vacua are dynamically accessible, and then a lot of "small" superselection sectors, in which string theory isn't so interesting. But there are so many unanswered questions: Do CY vacua even have holographic duals? What about topology change in the boundary? Are there "sectors" devoted specifically to de Sitter space (as Tom Banks suggests), or does dS get realized only as a fluctuation in AdS space?

It's also hard to say whether there will be much of a landscape in the realistic-looking sectors of string theory. Jacques Distler seems to think that there will be a landscape for values of the cosmological constant, but not necessarily for the standard model parameters. I believe he's thinking in terms of a high-genus CY space, with the standard model fields e.g. existing on branes wrapped around just a few of the cycles, and with the cosmological constant arising from branes wrapped on distant cycles which only interact gravitationally with our branes. This is a setup where the value of the cosmological constant can be anthropically selected, as suggested by Weinberg, because the topology etc of those distant cycles is independent of the local cycles, and the cosmological constant in this scenario is just the sum of many independent positive and negative components. But local structures, according to this argument, will be much more rigid.

As for the second reason - calculating the masses is simply difficult, even in a completely specified model - see the papers discussed in https://www.physicsforums.com/showthread.php?t=455180". The authors flatly state that they are unable to determine the masses, so for now all they do is show that the observed masses are within the available parameter space.

But this situation won't exist forever, and this brings me to a more esoteric reason for believing that masses aren't as tunable as you might think - the Koide relation between the electron, muon, and tauon masses, which is also mentioned in that thread, and which has occasionally been discussed in this forum. Very few particle physicists have even tried to build models that explain that formula, because there ought to be loop corrections to it coming from QED; yet it's still exact at low energies, so something must be cancelling those corrections. We may have little or no idea of what the explanation is, but if string theory can match reality, it will surely be by providing a mechanism that explains the formula, not just by matching the observed masses through three independent acts of fine-tuning. But the existence of such a mechanism means that the possible masses are more constrained than naive landscape thinking suggests.

 

[Physics Monkey]

I believe that the argument for a discrete space of solutions is the following. A point in the landscape is particular background where the scalar fields (moduli) have been fixed to their minima in some potential. One way to generate this potential is to add fluxes through compact cycles of the internal geometry of the background. But these fluxes are quantized, so in turn the moduli vevs depend on discrete parameters.

Thanks! This argument I understand, but how do we know that the potentials don't have compact flat directions like the mexican hat? And how much evidence do we have that the moduli potentials don't also depend on continuous parameters?

Non-SUSY vacua could be considered (I'm not implying control), but it depends on what question you want to ask and what scale you are working at. Usually one looks for theories with low-energy SUSY and the presence of a suitable Higgs sector. If SUSY is found at the LHC, it would at least confirm that such solutions are the ones to look for. It would be much harder to try to determine a landscape of nonSUSY theories at 1 GeV.

Since susy is highly non-generic from the point of view of field theory, I personally find it unconvincing to invoke low scale SUSYsusy. Even supposing susy were required at very high scales for consistency or something (quite a claim already), it seems to me that the vacua with susy breaking at a high scale will vastly outnumber the vacua with low scale susy breaking. I freely admit that I have no clean framework for making this statement, only the rough intuition that susy is highly non-generic, requiring the tuning of many relevant operators to zero. But if we accept that we'll generically be left with some strongly interacting non-susy gauge theory at high scales, well then I would imagine that computation of the masses will be next to impossible. Of course, if low energy susy is found then the story seems quite different as you say.

 

[Physics Monkey]

Factually, whether or not it can do this is unknown, for two reasons: we don't know the global structure of string theory, and small nonzero masses are apparently very hard to calculate in string models.

Certainly I agree that we don't know if string theory is capable of predicting masses, etc. But we also don't even know if string theory is the only possibility. Where do loops fit in? Are there other low energy theories containing gravity that are not liftable to string theory? I think none of these questions have even a remotely satisfactory answer. One of my main points is historical. It would truly be an unprecedented event in science should we somehow find ourselves able to bridge so many orders of magnitude in energy via a purely theoretical argument. I continue to suspect, as I think nearly all available evidence suggests, that we're just going to have to keep doing experiments all the way up to really find out what the cosmos looks like.

The AdS/CFT duality encourages me to think of string theory as consisting of a large number of separate quantum theories - you could think of them as different superselection sectors - one for each distinct boundary theory. Then you have the work by Brian Greene and others on how the space of CY manifolds is connected by conifold transitions (also see the much more recent work of Rhys Davies on "hyperconifold transitions"), which suggests one big theory. It's very unclear to me how it all comes together in the end. Maybe there are one or two "big" superselection sectors, in which a large number of different CY vacua are dynamically accessible, and then a lot of "small" superselection sectors, in which string theory isn't so interesting. But there are so many unanswered questions: Do CY vacua even have holographic duals? What about topology change in the boundary? Are there "sectors" devoted specifically to de Sitter space (as Tom Banks suggests), or does dS get realized only as a fluctuation in AdS space?

It's also hard to say whether there will be much of a landscape in the realistic-looking sectors of string theory. Jacques Distler seems to think that there will be a landscape for values of the cosmological constant, but not necessarily for the standard model parameters. I believe he's thinking in terms of a high-genus CY space, with the standard model fields e.g. existing on branes wrapped around just a few of the cycles, and with the cosmological constant arising from branes wrapped on distant cycles which only interact gravitationally with our branes. This is a setup where the value of the cosmological constant can be anthropically selected, as suggested by Weinberg, because the topology etc of those distant cycles is independent of the local cycles, and the cosmological constant in this scenario is just the sum of many independent positive and negative components. But local structures, according to this argument, will be much more rigid.

As for the second reason - calculating the masses is simply difficult, even in a completely specified model - see the papers discussed in https://www.physicsforums.com/showthread.php?t=455180". The authors flatly state that they are unable to determine the masses, so for now all they do is show that the observed masses are within the available parameter space.

Thanks for those links. I too like the duality and I too think that we have a lot to understand about the dynamics of the string landscape. But I would also say that before we go speculating about the nature of landscape dynamics in string theory, we should produce at least one vacuum which describes our world (maybe modulo the cosmological constant). I suspect that if and when this happens, we will immediately find a large number of similar looking solutions. But it would be very interesting either way. Personally, I find the reliance on susy and CYs is particularly disturbing given how non-generic susy is within the context of field theory (and the lack of it in our low energy world). It's fine to get your feet wet and to say wonderful non-perturbative things about gauge theory, but I think it's taken too seriously as a component of the actual high energy world. Of course, my opinion will obviously change should experimental evidence be forthcoming.

But this situation won't exist forever, and this brings me to a more esoteric reason for believing that masses aren't as tunable as you might think - the Koide relation between the electron, muon, and tauon masses, which is also mentioned in that thread, and which has occasionally been discussed in this forum. Very few particle physicists have even tried to build models that explain that formula, because there ought to be loop corrections to it coming from QED; yet it's still exact at low energies, so something must be cancelling those corrections. We may have little or no idea of what the explanation is, but if string theory can match reality, it will surely be by providing a mechanism that explains the formula, not just by matching the observed masses through three independent acts of fine-tuning. But the existence of such a mechanism means that the possible masses are more constrained than naive landscape thinking suggests.

This is the only statement that I'm not comfortable with. The Koide formula is amusing, but I'm willing to come out and say that I don't think its anything more at the moment. If someone comes along with a more coherent framwork then I would be happy to listen, but in my experience it just isn't that hard to produce such numerical coincidences. Especially in light of the fact that, as you point out, these masses come from low energy values of the yukawa couplings. If anything we might imagine that string theory produces nice geometrical relations at high energy which then flow at low energies to some random crap. In any event, speaking only for myself, I wouldn't place any weight on this formula as far as judging string prospects.

 

[fzero]

Thanks! This argument I understand, but how do we know that the potentials don't have compact flat directions like the mexican hat? And how much evidence do we have that the moduli potentials don't also depend on continuous parameters?

There are two sources of flat directions. First, a scalar field may have no potential at all, so it is not fixed. Second, we can have a compact flat direction when the potential depends only on the complex modulus $$|\phi_i|$$ so that the phase does not appear in the potential. In a supersymmetric theory, we have superpotentials. These are holomorphic, so as long as a scalar field enters into the superpotential, so does its phase. As long as the F-flatness conditions can be solved, the phases will be fixed when we compute the roots of the superpotential. There won't be any flat directions.

I think the only caveat to the above argument is if a field only enters into the superpotential linearly, so that there is no mass term. In this case we cannot guarantee that the F-flatness conditions fix the value of the field.

So the challenge is simply to generate a superpotential that contains all moduli. For IIB complex structure moduli, this is rather simple. The presence of 3-form flux generates a term

$$W_G \sim \int_X G^{(3)}\wedge \Omega(z_i) ,$$

where the $$(3,0)$$-form $$\Omega(z_i)$$ depends on all complex structure moduli. I think it's generic that mass terms are generated from this formula, since $$\Omega$$ depends quadratically on the covariantly constant spinor, so should be at least quadratic in the $$z_i$$.

It is a bit more difficult to compute the superpotential for Kaehler moduli, since it is nonperturbative, but there are solid constructions such as http://arxiv.org/abs/arXiv:1003.1982 that stabilize all Kaehler moduli.

Since susy is highly non-generic from the point of view of field theory, I personally find it unconvincing to invoke low scale SUSYsusy. Even supposing susy were required at very high scales for consistency or something (quite a claim already),

Well low scale SUSY is not something created by string theorists, but by phenomenologists that want to solve the hierarchy problem. Of course, SUSY makes computations much easier, but there is a strong motivation in the absence of direct evidence.

it seems to me that the vacua with susy breaking at a high scale will vastly outnumber the vacua with low scale susy breaking. I freely admit that I have no clean framework for making this statement, only the rough intuition that susy is highly non-generic, requiring the tuning of many relevant operators to zero.

I'm not that big on promoting the landscape, but from that perspective, the relative paucity of vacua with low-scale SUSY would be encouraging, if in fact low-scale SUSY is found in nature. It's hard to make other suggestions, since in the absence of a selection mechanism, we don't really know whether SUSY is preferred or not.

But if we accept that we'll generically be left with some strongly interacting non-susy gauge theory at high scales, well then I would imagine that computation of the masses will be next to impossible. Of course, if low energy susy is found then the story seems quite different as you say.

Yes, it's clear that SUSY, at the moment, is crucial to computations. This problem would likely face any theory that spit out an effective field theory a few orders of magnitude below the Planck scale.

 

[MTd2]

Couldn't entropy minimizing processes like those that happen with protein folding be happening with the choice of our vacuum out of all those of string theory?

 

[Haelfix]

Question: why do you think that dS space does not exist as a full quantum theory? (what does that mean exactly?) Is it based on string theoretic reasing, or are there more general ideas?

Yea, so it seems to be much more general but still a highly active research direction and extremely subtle.

The problem with doing quantum gravity in DeSitter space are numerous, basically all stemming from the fact that there lacks a notion of what a good observable is and so asking questions of the theory becomes a sort of tortured process where you have to invent meta observables or chop the space up into causal patches where you can kind of wave your hands to make arguments.

Witten wrote a famous paper summarizing much of what is known about quantum gravity in DeSitter space and I highly recommend reading it, b/c it is absolutely beautiful and illustrates most of the problems with quantum gravity in general.
arXiv:hep-th/0106109

So you probably know that when you include gravity quantum mechanics has no local observables. However you can kind of make sense of affairs by thinking about asymptotic observables (work by De Witt in the early days of QG). Even there things are subtle (this touches on the question on the GR thread about large diffeomorphisms), and particularly so in quantum gravity where there is simply no other choice and any test probe causes fluctuations to the actual gravitational field and thus perhaps the actual superselection sector itself! How you dance around this is very subtle.

Anyway in so far as this makes sense you can derive an Smatrix in the case where lambda = 0, (where there is a natural null boundary) with the right type of properties that you might expect and so that is relatively nice. In the case lambda < 0, you don't have an SMatrix, but there is a conformal boundary and correlator functions that can serve as natural observables. This has of course been utilized in the AdS/CFT correspondance.

By contrast in De Sitter space, the only available boundaries (I think they are often called Scri + -) are in the infinite past and infinite future, and no observer has access to the full information of the theory or has access to any type of a conserved quantity like energy. Now for various reasons (entropy etc), various authors (Banks, Fisher, Susskind et al) have argued that DeSitter space does not carry a Hilbert space in the usual sense of the word, but instead only possesses a finite Hilbert space of states:
arXiv:hep-th/0212209

This of course is pretty bad on physical grounds, and strongly implies the loss of a classical limit. How you resolve this is of course the open question and caused (and still causes) a tremendous amount of confusion in theorist circles.
One way of doing it is by taking a queue from inflation theory where it was understood long ago that there are instanton processes that allow you to tunnel out of false vacuums, and in particular DeSitter spaces where you need to exit inflation into the reheating phase. Further the timescales are so large in Eternal De Sitter space, that such ridiculously rare events can in fact (nay, must) happen, further implying that eternal ds might not be the end state! There are many proposals for how to do this, but this Arkani Hamed et al paper is also worth checking out (with a good review):

arXiv:0704.1814

 

[Fra]

So you probably know that when you include gravity quantum mechanics has no local observables. However you can kind of make sense of affairs by thinking about asymptotic observables
...
By contrast in De Sitter space, the only available boundaries (I think they are often called Scri + -) are in the infinite past and infinite future, and no observer has access to the full information of the theoryor has access to any type of a conserved quantity like energy.
...
This of course is pretty bad on physical grounds, and strongly implies the loss of a classical limit. How you resolve this is of course the open question and caused (and still causes) a tremendous amount of confusion in theorist circles.

Thanks Haelfix for your always excellent posts.

I think thse are excellent conceptual points we all should keep on a postit on our foreheards to make sure we don't loose contact with the real questions.

These are exacly the foundational measurement issues we must not hide from - that fact that there is no reasonable way to save a classical observer. This only works for subsystems, when asymptotic observables of course makes perfect sense. I really like when one doesn't try to cover up these conceptual issues in smoke of mathematical beauty detached from the original problems.

/Fredrik

 

[Physics Monkey]

There are two sources of flat directions. First, a scalar field may have no potential at all, so it is not fixed. Second, we can have a compact flat direction when the potential depends only on the complex modulus $$|\phi_i|$$ so that the phase does not appear in the potential. In a supersymmetric theory, we have superpotentials. These are holomorphic, so as long as a scalar field enters into the superpotential, so does its phase. As long as the F-flatness conditions can be solved, the phases will be fixed when we compute the roots of the superpotential. There won't be any flat directions.

I think the only caveat to the above argument is if a field only enters into the superpotential linearly, so that there is no mass term. In this case we cannot guarantee that the F-flatness conditions fix the value of the field.

So the challenge is simply to generate a superpotential that contains all moduli. For IIB complex structure moduli, this is rather simple. The presence of 3-form flux generates a term

$$W_G \sim \int_X G^{(3)}\wedge \Omega(z_i) ,$$

where the $$(3,0)$$-form $$\Omega(z_i)$$ depends on all complex structure moduli. I think it's generic that mass terms are generated from this formula, since $$\Omega$$ depends quadratically on the covariantly constant spinor, so should be at least quadratic in the $$z_i$$.

Ok, I like the holomorphy argument, but just so I completely understand your thinking:
1. If we considered non-susy solutions than flat directions would be generic?
2. Is it believed that the holomorphic superpotential cannot depend on continuous parameters i.e. only on discrete fluxes?

Well low scale SUSY is not something created by string theorists, but by phenomenologists that want to solve the hierarchy problem. Of course, SUSY makes computations much easier, but there is a strong motivation in the absence of direct evidence.

Certainly, I didn't mean to imply string people started low scale susy. Personally, I'm not sure exactly how strong the motivation is for low scale susy from a purely particle point of view. The talks I've heard are very unconvincing, and purely from the point of naturalness w/o a priori susy, susy requires all kinds of unnatural fine tuning. It's an attractive idea if you like symmetry, but I've never quite understood the hold it has over phenomenologists. Regardless, my personal prejudices are beside the point.

I'm not that big on promoting the landscape, but from that perspective, the relative paucity of vacua with low-scale SUSY would be encouraging, if in fact low-scale SUSY is found in nature. It's hard to make other suggestions, since in the absence of a selection mechanism, we don't really know whether SUSY is preferred or not.
Yes, it's clear that SUSY, at the moment, is crucial to computations. This problem would likely face any theory that spit out an effective field theory a few orders of magnitude below the Planck scale.

Right, but if low scale susy is not found, and the landscape turns out to contain many more vacua without low scale susy, then would you agree that things look much less hopeful? We'll be faced with the hard quantum field theory problem you mention of taking the effective theory at high scales and bringing it to low energies, and there may be many ways to approximate our world.

 

[fzero]

Ok, I like the holomorphy argument, but just so I completely understand your thinking:
1. If we considered non-susy solutions than flat directions would be generic?

I haven't checked that anything fundamentally changes if the F-terms get vevs. My intuition is that flat directions tend to occur when moduli only appear linearly in the potential. Regardless of where they occur, I do believe that these flat directions are always lifted at 1-loop. I did browse through some old reviews when I was writing the previous post and couldn't find any definite statements of lore though.

2. Is it believed that the holomorphic superpotential cannot depend on continuous parameters i.e. only on discrete fluxes?

There are no free parameters in the string theory, so any such continuous parameters would be a mystery. The superpotential can only depend on the moduli (geometric+dilaton) and the fluxes. There could be additional terms in the superpotential besides the one I wrote down (these would tend to be some nonperturbative physics), but there aren't any new parameters that we know of.

Right, but if low scale susy is not found, and the landscape turns out to contain many more vacua without low scale susy, then would you agree that things look much less hopeful? We'll be faced with the hard quantum field theory problem you mention of taking the effective theory at high scales and bringing it to low energies, and there may be many ways to approximate our world.

Yes, I agree that things will get difficult and people will have to try to solve harder problems. I'm not sure that the problem will be more or less difficult than what would have to go into a selection mechanism anyway. I suppose more of an emphasis will be placed on holographic descriptions, which haven't been used much in this context.

 

[smoit]

1. If we considered non-susy solutions than flat directions would be generic?
2. Is it believed that the holomorphic superpotential cannot depend on continuous parameters i.e. only on discrete fluxes?

1. It's the other way around. Flat directions in the moduli space are generic with unbroken SUSY. Once SUSY is broken spontaneously, flat directions are generically lifted by the radiative corrections, unless there is a shift symmetry that protects them, e.g. the axionic directions cannot get masses at the perturbative level but eventually get lifted non-perturbatively.

2. The superpotential does depend on continuous parameters - the moduli, as well as discrete parameters such as fluxes. However, the moduli are not fundamental parameters. They are fixed once you minimize the scalar potential and find a local minimum. The moduli vevs at the minimum will be given in terms of the integer fluxes or other discrete dials that enter the superpotential.

Just to be clear, one of the main reasons for considering flux compactifications in Type IIB orientifolds (by Giddings Kachru and Polchinski) was to construct strongly warped solutions where the gauge hierarchy problem could be addressed a la Randall Sundrum.

The main problem with flux compactifications is the large (in string scale units) value of the flux superpotential. It's a tree-level contribution and getting a small gravitino mass (the order parameter for spontaneous SUSY breaking that sets the overall scale of superpartner masses) requires some 15 orders of magnitude of fine tuning . Low scale susy is much more natural in fluxless G2 compactifications of M-theory, where one can stabilize all moduli non-perturbatively and the large hierarchy of scales can be easily generated. The reason for the superpotential being purely non-perturbative is the PQ-type shift symmetry, inherited from the gauge symmetry of the 11-D supergravity 3-form, which all the complexified moduli possess. This symmetry automatically forbids any perturbative contributions to the superpotential but can be broken by non-perturbative effects, i.e. gaugino condensation or the membrane instantons. So, the scale of susy breaking is given by
$$m_{3/2}\sim\frac{\Lambda^3}{M_{Planck}^2}$$, where $$\Lambda \sim M_{Planck} e^{- \frac {2\pi Vol}{3N}}$$ is the strong coupling scale of some hidden sector SU(N) SYM gauge theory and $$Vol$$ is the stabilized volume of a supersymmetric three-cycle supporting the hidden sector gauge theory.

 

[suprised]

Last but not least my feeling is that at a rather early stage there was a wrong turn (I cannot tell exactly which one) which prevents us from asking the right questions. ...
Perhaps there are string theorists here able to tell us what could have been this wrong turn in the very beginning.

I guess there were many potentially wrong turns - at least in the sense of bias towards certain ways of thinking about string theory. Here a partial list of traditional ideas/beliefs/claims that have their merits but that potentially did great damage by providing misleading intuition:

- That geometric compactification of a higher dimensional theory is a good way to think about the string parameter space
- That perturbative quantum and supergravity approximations are a good way to understand string theory
- That strings predict susy, or have an intrinsic relation to it (in space-time)
- That strings need to compactify first on a CY space and then susy is further broken. That's basically a toy model but tends to be confused with the real thing
- That there should be a selection principle somehow favoring "our" vacuum
- That a landscape of vacua would be a disaster
- That there exists a unique underlying theory
- That things like electron mass should be computable from first principles

Most of these had been challenged/revised in the recent years, and many people think quite differently about them than say 15-20 years ago.

 

[Physics Monkey]

1. It's the other way around. Flat directions in the moduli space are generic with unbroken SUSY. Once SUSY is broken spontaneously, flat directions are generically lifted by the radiative corrections, unless there is a shift symmetry that protects them, e.g. the axionic directions cannot get masses at the perturbative level but eventually get lifted non-perturbatively.

Thanks, I think I understand your point. I suspect I was more thinking about a situation where the coefficients of the potential depend on other parameters which themselves have a continuum range and an unbroken shift symmetry (except spontaneously).

 

[marcus]

Suprised, I think this #523 of yours is a truly enlightening post. Potentially it puts the String approach in a much more attractive light for many of us.
For context, I will excerpt the post by Tom Stoer that you were responding to, and then copy your post, which I would like to study and ask a question about.

Last but not least my feeling is that at a rather early stage there was a wrong turn (I cannot tell exactly which one) which prevents us from asking the right questions. This is our blind spot.
...

String theory (as any other theory) limits our ability to ask questions. w/o further experimental input we are stuck. In the standad model we can ask questions regarding the Higgs boson. We can even ask questions regarding alternative mechanisms and we are not stuck once the LHC shows that there is no Higgs boson.

Now the problem is that I can only say that at a very early stage in string theory we may have chosen the wrong direction. From that point onwards we lost the ability to ask questions which would enable us to overcome the blind spot of string theory.

Now let's talk about other theories, like LQG. I don't want to promote LQG as the alternative theory to string theory in sthe sense that it has the ability to achieve unification of forces. I don't think so. I am simply saying that LQG is able to ask different questions. LQG is able to ask questions regarding an algebraic spacetime structure. This question is (afaik) not pronounceable in the language of string theory (maybe I am wrong; I am not an expert on matrix models).
...
Perhaps there are string theorists here able to tell us what could have been this wrong turn in the very beginning.

[EDIT: I have numbered your 8 possible "wrong turns" for easy reference.]
===quote Suprised===
I guess there were many potentially wrong turns - at least in the sense of bias towards certain ways of thinking about string theory. Here a partial list of traditional ideas/beliefs/claims that have their merits but that potentially did great damage by providing misleading intuition:

1. - That geometric compactification of a higher dimensional theory is a good way to think about the string parameter space
2. - That perturbative quantum and supergravity approximations are a good way to understand string theory
3. - That strings predict susy, or have an intrinsic relation to it (in space-time)
4. - That strings need to compactify first on a CY space and then susy is further broken. That's basically a toy model but tends to be confused with the real thing
5. - That there should be a selection principle somehow favoring "our" vacuum
6. - That a landscape of vacua would be a disaster
7. - That there exists a unique underlying theory
8. - That things like electron mass should be computable from first principles

Most of these had been challenged/revised in the recent years, and many people think quite differently about them than say 15-20 years ago.
==endquote==

I get the impression that these 8 ideas of what could have been a false step (or no longer useful way of thinking) offer a way that the String program can re-energize and get on a more creative footing. Looking particularly at your #1.

It could be limiting to imagine certain degrees of freedom as actual spatial dimensions. Now, you suggest, modern String researchers do not think of space as having extra dimensions. (Rolled-up compactified extra dimensions of space are maybe only in popularization books and the public's mind.)

So how do contemporary researchers think of these extra degrees of freedom? If #1 was a "wrong turn" then could you say a little bit about what a better turn might be, at this point?

 

[tom.stoer]

Very interesting list. What I miss is the "fixed background"; or is this implicitly contained in 2.?

 

[marcus]

Very interesting list. What I miss is the "fixed background"; or is this implicitly contained in 2.?

I should wait for Suprised to respond, but I'm compelled to say that #2 strikes me as a blockbuster. If as he says "many" in the String community "think quite differently about [point #2] than say 15-20 years ago," then doesn't this mean that they want to move away from perturbation around prior fixed geometric background?
I only fear that their only "out" is via AdS/CFT, which is limiting in its own way. I hope that what Suprised means is that some are making a determined effort to find some other way of breaking away from the fixed geometry framework.