Since string theory first became popular in 1984-5, attempts to connect it to particle physics have suffered from various problems. One of the most severe of these goes under the name of “moduli stabilization”. Six dimensional Calabi-Yau manifolds come in families, parametrized by “moduli”. The dimensions of these moduli spaces can be of order 100 or so.

Naively it might appear that string theories are characterized by a choice of a topological class of Calabi-Yaus (no one knows if the number of these is finite or infinite), and then a choice of each of the 100 or so parameters that fix the size and shape of the Calabi-Yau. According to the standard string theory ideology, this is not the right way to think, instead there is really only one string theory, with different moduli values corresponding to different states. The moduli parameters are supposed to be dynamical elements of the theory, not something parametrizing different theories.

The problem with this is that if you promote the moduli to dynamical fields, they naively correspond to massless fields, and thus give new long-range forces. So you have to explain away why we don’t see 100 or so different kinds of long-range forces, and the experimental bounds on such forces are very good. Some kind of dynamics must be found that will “stabilize moduli”, giving them a non-trivial potential. The moduli fields will then be fluctuations about the minima of this potential. If the quadratic piece of the potential is large enough, their mass will be high enough to have escaped observation.

One needs a potential with non-trivial minima, and has to ensure that the dynamics is not such that the moduli will run off to infinity. In recent years, ways of achieving this have been found that typically involve “flux compactifications”, i.e. choosing non-trivial fluxes through the topologically non-trivial holes in the Calabi-Yau. On the one hand, this seems to provide a long-standing solution to the problem of how to stabilize the Calabi-Yau, on the other hand, it appears that there is an exponentially large number of possible minima. This is the origin of the “Landscape” and the associated claims of 10^{500} or more possible vacuum states for string theory.

The constructions involved are famously exceedingly complex and ugly, with Susskind referring to them as “Rube Goldberg machines”, and one of their creators, Shamit Kachru, the “Rube Goldberg architect”. Very recently a new Reviews of Modern Physics article by Kachru and Douglas called Flux Compactification has appeared. It can be thought of as a manual describing how to construct and count these Rube Goldberg machines.

Many string theorists had long hoped that whatever method was found to stabilize moduli would have only a small number of solutions. Then, in principle one would get only a small number of possible models of particle physics for each topological class of Calabi-Yaus. If the number of these was finite and not too large (the known number of constructions is something like 10^{5}-10^{6}), then to see if string theory could make contact with particle physics, one would just have to do a moderately large number of calculations, check them against the real world, and hope that one matched. If it did, it would then be highly predictive.

The existence of the flux compactifications with stabilized moduli described in the Douglas-Kachru article has convinced many string theorists that this old dream is dead. Some have tried to claim that this is a good thing, that the exponentially large number of states allows the existence of ones with anomalously small cosmological constants, and thus an anthropic explanation of its value. The problem then becomes one of how to ever extract any prediction of anything from string theory. Small CCs are achieved by very delicate cancellations, and it appears to be a thoroughly calculationally intractable problem to even identify a single state with small enough CC.

Many string theorists are now claiming that this is not really a big deal. So what if there are lots and lots of string theory vacua, it’s just like the fact that there are lots and lots of 4d QFTs! For arguments of this kind, see recent comment threads here and here. There’s something fishy about this argument, since discussion of flux compactifications has from the beginning focused on whether it is possible to use them to make predictions, whereas no one ever was worrying about whether (renormalizable) QFTs were predictive or not.

The source of the problem lies in the combination of the large numbers of string theory vacua with their Rube Goldberg nature. Consistent 4d QFTs are characterized by a limited set of data (gauge groups, fermion and scalar representations, coupling constants), and it has turned out that among the simplest possible choices of such data lies the Standard Model. String theorists commonly describe the Standard Model as “ugly”, but it is among the simplest possible 4d QFTs, and is extremely simple and beautiful compared to something like the flux compactification constructions. One could hope that while flux compactifications are inherently rather complicated, one of the simpler ones might correspond to the real world. As far as I know there’s no evidence at all for this, such a hope appears to have nothing behind it besides pure wishful thinking. Some string theorists like Douglas and Kachru don’t seem to think this is possible, focussing instead on statistical counts of more and more complicated flux compactifications, hoping to find not a simple one that will work, but a statistical enhancement of certain complicated ones that would pick them out.

4d QFT is a predictive framework not because the number of possible such QFTs is small, but because our universe is described extremely accurately by one of a small number of the simplest of such QFTs. A few experiments are sufficient to pick out the right QFT, and then an infinity of predictions follow.

Is the QFT framework falsifiable? One could imagine that things had worked out differently, that instead of the Standard Model predictions being confirmed, each time a new experimental result came in, one could only get agreement with experiment by adding new fields and interactions to the model. It might very well be that the QFT framework could not be falsified, since one could always evade falsification by adding complexity. This happens very often with wrong ideas: they start with a simple model, experimental results disagree with this, but can be matched by making the model more complicated. As new experiments are done, if the original idea is wrong, it doesn’t get simply falsified, but the increasing complexity of the models needed to match experiment sooner or later causes people to give up on the whole idea.

This is very much what has happened with string theory. The simple models that got people excited about the idea of string theory unification don’t agree with experiment, with the moduli stabilization problem just one example. It appears one can solve the problem, but it’s a Pyrrhic victory: one is forced into working with a class of models so vast and so complicated that one can get almost anything, and never can extract any real predictions.

Douglas and Kachru do address the question of whether one can ever hope to get predictions out of this class of models, but their answer is that they can’t think of any plausible way of doing so. They mention various things that people have tried, but none of these ideas seem to work. The best hope was that counting vacua with different supersymmetry breaking scales would lead to a statistical prediction of this scale, but this has not worked out for reasons that they describe. In the end they conclude:

*For the near term, the main goal here is not really prediction, but rather to broaden the range of theories under discussion, as we will need to keep an open mind in confronting the data.*

This acknowledges that no predictions from this framework seem to be possible, and that continuing work in this area just keeps producing yet wider and wider classes of these Rube Goldberg machines. They are suggesting basically giving up not on string theory, which would be the usual scientific conclusion in this circumstance, but instead to for now give up on the theorist’s traditional goal of making testable predictions. They advocate not giving up on string theory no matter how bad things look, instead just continuing as before, hoping against hope that an experimental miracle will occur. Maybe astronomers will find evidence for cosmic superstrings, maybe the LHC will see strings or something that matches up with characteristics of one of the Rube Goldberg models. There’s not the slightest reason to believe this will happen other than wishful thinking, which has now been promoted to a new program for how to do fundamental science.

**Update**: Via Lubos, for those who don’t know what a Rube Goldberg machine is, two examples are here and here.

>> This is very much what has happened with string theory.

You are factually incorrect. The flux vacua were always there, it just took researchers some time to realize it. No one has ever added a single complication to string theory, because it is not possible. If you want to discover something in string theory it had better be there in the first place.

Michael said (sort of):

You are factually incorrect. The flux vacua were always there, it just took our brothers some time to realize it. No one has ever added a single complication to the Bible, because it is not possible. If you want to discover something in the Bible it had better be there in the first place.

Hallelujah, brother Michael

Michael is right: this problem could have been realized or advertized many years ago, and he would have spent all these years working on something better. This situation can be extremely disappointing, but it is not Peter’s fault. So, please stop fighting on each word.

Dear Peter,

I strongly disagree with your claim that

>one is forced into working with a class of models so vast and so complicated >that one can get almost anything, and never can extract any real predictions.

In the IIB flux framework there is by now a substantial literature on studying supersymmetry breaking, computing soft terms, running them down to the TeV scale and analysing the phenomenology of the resulting sparticle spectrum.

There are also `generic’ results: if moduli are stabilised by non-perturbative effects, as occurs in all these models, the moduli mass is lifted above the gravitino by a factor ln(M_P/m_{3/2}) while the corresponding gaugino mass is lowered by a similar factor.

Generally different methods of moduli stabilisation are quite specific, and have typical outcomes and mass scales, and I do not see any evidence at a technical level for the claim that one can get almost anything.

Best wishes

Joe Conlon

Peter,

“It might very well be that the QFT framework could not be falsified, since one could always evade falsification by adding complexity.”

The framework of QFT is of cause falsifiable. One of the proud achievements of particle theory of the 50s and 60s was the derivation of structural consequences of micro-causality: the adaptation (rigorous derivation from the principles, not just perturbative checks) of the Kramers-Kronig dispersion relation. The experimental check in high-energy scattering experiments was carried out and QFT passed with flying flags. Micro-causality is the epitome of QFT and the experimental test of dispersion relations is one of the finest falsifiability tests of QFT (would have been worthwhile to be mentioned in your book, but by the time you entered physics this nice conquest was already taken for granted).

With specific models of QFT this is of course harder since in the present state of developments there are no hard (nonperturbative) facts one can abstract from Lagrangian names (or similar model characterizations) if one still does not know whether there is a living child behind that name (this is of course infinitely worse in ST).

A good illustration of this difficulty is the previous discussion (with David Berenstein) about the AdS–CFT structural theorem (crystal-clear) and the Maldacena conjecture (which is a statement about one of those baptized models in the limit N–>infinity where it slips out of the framework of QFT).

There are myriads of QFTS, need experiment to make the choice. There are myriads of flux compactifications, need experiment to make the choice. It sounds fishy but the fishiness is elusive. If we forget that low energy physics was supposed to be a prediction of string theory, and simply say, here are two methods of constructing models – QFTs, string compactifications – and there are many choices in each – where is the fishiness in that?

Somehow there is a difference between pre-Revolution and post-Revolution thinking, but I can’t put my finger on it.

Let us imagine that string theory is true and we live in a multiverse. Let us imagine, in a science-fiction way, we are able to communicate with intelligent agents in another universe. Suppose our task is to find out what is the low energy content of that other universe. We are provided the results of collider experiments from that other universe and to request specific experiments be performed. We would build the model via QFT, not via flux compactification – even though flux compactification is the “true” !

The clear lesson of this entire episode is that one cannot do physics by exhaustion of a mathematical idea. The world has to guide the choice of ideas, the ideas cannot be forced onto the world. A corollary is that a successful idea must be backed up by a clear metaphysics – both quantum theory and relativity needed Democritus first.

My personal hero in the history of science is Kepler. He did not allow his personal love for his shell model, based on the regular Platonic solids, to stand in the way of dealing with the facts. Even more than Bacon, this set the tone for how to do science. Invent, but pay attention.

-drl

Joe,

Are you claiming that you always will get the relation between moduli, gravitino and gaugino masses that you mention? So, if we measure these masses and don’t see this relation, string theory is just incorrect?

Or, are there some vacua where this relation isn’t true?

Dear Peter,

My comment applied for the IIB flux vacua, where complex structure moduli are stabilised by fluxes and the K\”ahler moduli are stabilised by non-perturbative effects. It is these vacua which are the principal basis for the claims about the landscape. If this small logarithmic hierarchy does not exist, then I do not see how these vacua can describe nature.

The point is that although there may be 10^500 ways of turning on fluxes, that doesn’t mean that every feature of the low energy theory can take 10^500 values: there can be, and are, aspects that are insensitive to the fluxes.

There are string vacua where this relation isn’t true – for example exactly supersymmetric compactifications or if you stabilise moduli perturbatively.

Best wishes

Joe

As a person who used to work on this subject and switched to more formal problems in ST, let me make the following comments.

1) Flux compactifications exist in the literature since the 1996 paper of Polchinski and Strominger and were ignored for a long time for a very good reason: they have no CFT description, therefore they are not “calculable” by using standard ST techniques.

2) Around 2001 several respected string theorists, including Kachru, largely ignored this problem (or argued that in some special cases one can circumvent it) and started using the effective field theory description (EFT) for moduli stabilization etc. Then Douglas started counting such EFT vacua, and the landscape bandwagon took off (taking with it a whole generation of students).

3) It should be made clear that 99.9% of work on flux compactification, including those of the authors of the review, KKLT, Joe’s etc, is made within (quite an eclectic) EFT.

4) There is no reason to believe that EFT is a good (or any type of) approximation because alpha’ and loop corrections are out of control — we simply do NOT know how to compute them, so there is no reason to believe that the landscape of 10^??? vacua really exists. I can guarantee the existence of only one “non-standard-model” ST vacuum: maximally supersymmetric toroidal compactification.

4) In conclusion, the landscape has no solid theoretical foundations and can be safely ignored. If you are seriously interested in these topics, you should work on developing a full-fledged ST description of flux compactifications (RR backgrounds etc…)

Dear T.,

I find this statement a bit odd,

>4) There is no reason to believe that EFT is a good (or any type of) >approximation because alpha’ and loop corrections are out of control — we >simply do NOT know how to compute them, so there is no reason to believe >that the landscape of 10^??? vacua really exists.

Effective field theory has been used in discussions of string compactifications ever since the subject started, so I don’t see any principled objection to its use in flux compactifications that doesn’t also apply to its use in (say) old-style unfluxed heterotic models.

With regard to alpha’ and loop corrections, I don’t see what is wrong with the conventional statement that in a regime of large volume and weak coupling, the alpha’ and g_s expansions are ordinary weak-coupling perturbation expansions, and so can be controlled.

Best wishes

Joe

Joe,

Even if alpha’ corrections are “small” in what you call “large volume” limit, you cannot prove that they do not destabilize the vacuum. Landscape counts all vacua, with {\em massless} moduli — and these can be destabilized by “infinitesimal” corrections. On the other hand, if you construct a model with all moduli (including large volume) stabilized (i.e. massive) then your EFT calculations make sense, similarly to old heterotic constructions involving gaugino condensation (assuming that the dilaton is stabilized in the weak coupling regime, which is very difficult to achieve). But then it’s not landscape — it’s model-building.

Dear Joe,

being (for a good reason) quite ignorant about how fluxes and nonperturbative effects stabilize the moduli of a type IIB model my naive question is: Where do the fluxes come from, what governs THEIR dynamics (I guess only their existence is guaranteed by topological arguments) and what precisely hides behind the mysterious-sounding term `nonperturbative effects´?

By the way, the reason why I don’t even believe in supersymmetric field theory and the SM’s Higgs mechanism

is the emergence of spin-1/2 excitations in the completely

confining phase of pure SU(2) or SU(3) YM. The mass of the stable and charged excitation essentially is given by the Yang-Mills scale . I have not yet an answer to the question why Yang-Mills scales are set into a hierarchical pattern but I’m pretty much convinced of the nonexistence of gauginos, gravitinos, sfermions, and fundamental scalars and SCALARINOS.

With my best regards, rh

Hi Peter;

Im an electrical engineer, but Im really fascinated by physics. I have read your book and that of Smolin. I really find it hard to imagine that even with (Sociology) and its dynamics, the physics community can be so naive. How can Witten et al, be allured and not know it, if the facts are so clear to you and others. What do they have to say to what you call a naive assumption about the moduli? if even a Fields medalist agrees to use it, how come ?

Ahmad,

I don’t know what Witten thinks of these flux compactifications. He hasn’t worked on them, my unsubstantiated guess would be that he would like them to not exist or find a reason to show that they aren’t real vacua of string theory, but he doesn’t know how.

I think the whole idea of trying to get physics out of these things is clearly unworkable, and I suspect more than a few string theorists feel the same way. Quite a few of them definitely don’t work on this area, and generally don’t want anything to do with it. The problem for them is how to answer the argument that these things are something that string theory seems to inevitably lead to. Commenter “T” here gives one attitude towards this.

Actually, Witten wrote one of the foundational papers on flux

compactifications (arXiv:hep-th/9906070) with Gukov and Vafa.

And almost all string theorists have worked on the subject, as the

gravity duals of field theories arising in AdS/CFT are flux vacua, the

simplest being AdS five times a 5 sphere.

anonymous,

I was referring not to general flux compactifications, which would include AdS/CFT, but to the ones discussed in the Douglas-Kachru paper as providing a way to stabilize moduli.

Thanks for the reference to the Gukov-Vafa-Witten paper. Again, I was thinking of the more recent constructions with stabilized moduli, but you’re right to point out that that is part of the story.

The GVW paper is actually about precisely the kinds of fluxes used in the moduli potentials. Witten wrote more papers about this (eg about G2 models with flux). So did Vafa.

And, the fluxes that are crucial in confining examples of AdS-CFT, are precisely used in the moduli fixing constructions. See Klebanov-Strassler.So, the subject cannot be divided up between AdS CFT fluxes, and the ones used in the constructions you dislike.

You are wrong. The GVW abstract reads:

“We consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi-Yau four-fold.” Lanscape studies are based on IIB orientifold compactifications to four dimensions, focussed on totally different aspects of compactifications.

Look up the meaning of f theory. The f theory compactifications to 4d are another name for IIB orientifolds in 4d at generic points in their moduli space. The GVW superpotential is the one used in ALL these models, with equal justification.

Dear T.,

>On the other hand, if you construct a model with all moduli

>(including large volume) stabilized (i.e. massive) then your EFT

>calculations make sense,

But this is what almost all/most/a lot of the work on the `landscape’ is about. As soon as you have the Gukov-Vafa-Witten superpotential, you are stabilising the dilaton and complex structure moduli, and then nonperturbartive terms come in to stabilise the K\”ahler moduli. You have to check the EFT for consistency.

I do agree with you that this is basically model-building, and I think that is a good thing,

Best wishes

Joe

… not even wrong, Joe…

To F-theory/orientifold expert: your attitude of deciding what research direction is good based on associations with W et al is exactly what ruined ST. Just try to think, maybe it’s not late for you to start thinking independently. Otherwise hide in Langlands. Good luck.

Peter, nice post, and thanks for the link to the review by Douglas and Kachru. It’s very nicely written. The authors definitely do not hide behind technichalities, so even non-experts like myself can learn much about the ideas and the status of the field from them.

Joe,

Of course, model-building is very interesting and useful. However, most of the remaining 10^??? vacua will never be investigated in such detail, and the debate is whether they really exist in full-fledged ST. The 10^??? counting includes all possible vacua with massless moduli: my hope is that they will turn out to be inconsistent, in a similar way as non-supersymmetric closed ST is inconsistent beyond one loop (due to the dilaton tadpole).

T:

A cursory reading makes it clear that the vacua being counted have no massless moduli, and even looking just at those with weak (stabilized) coupling, there are a huge number. They aren’t counting moduli spaces with unfixed moduli.

Jean Paul:

Actually I am just going through the review, I don’t know or care what W thinks. The logic seems clear, and also seems to extend beyond f theory to other regimes of string theory.

My cursory reading of the review is very different from yours, so let’s try to clarify it. Let’s look at page 47, subsection VB of section V “Statistics of vacua”. It considers IIB on CY with no complex structure moduli, ignoring Kahler moduli. I am no expert in CY, so can you tell me how many CY have no complex moduli, and zero Kahler moduli? I see that you are a big fan of GVW, but their superpotential can stabilize only the dilaton and some complex structure moduli. In order to stabilize Kahler moduli, you need D-terms, so you need magnetized D-branes, Joe’s non-perturbative effects etc. It’s not so simple. As far as I can tell ALL vacua treated so far statistically contain massless moduli, so please correct me if I am wrong. All what I am trying to say is that one needs a better understanding of flux compactifications before jumping to a conclusion that ST in inherently unpredictive and needs a special treatment by antropic reasoning etc.

T:

The KKLT construction fixes the Kahler moduli; explicit e.g.s are

given now by several groups cited in the review. The statistics Douglas et al give for complex moduli can be used in any of the models with fixed Kahler moduli, and as long as the flux potential isn’t too large, doesn’t destabilize the Kahler moduli. That is indeed the entire point of the KKLT construction of the landscape. As I read it, in the IIA theory, even just the fluxes suffice to stabilize all of the moduli; the analogue of the GVW superpotential depends on all moduli at tree level.

To be clear: this isn’t just my reading of the review , see their citations to

Douglas Denef Florea; Douglas Denef Florea Grassi Kachru;

Lust Reffert Scheidegger Schulgin Stieberger; Balasubramanian, Berglund, Conlon, Quevedo;

and for IIA

DeWolfe Giryavets Kachru Taylor; Acharya Benini Valandro;

Derendinger Kounnas Petroupoulos Zwirner; Camara Font Ibanez.

These papers have lots of equations and seem to do what the review says they do. Which is stabilize all the scalars.

This is an excellent post, Peter, and so is the discussion.

If I understand correctly the non-technical parts it appears that people

agree that the landscape is a problem for (or a challenge to) ST. There is a

comment though that the evidence for the huge number of vacuua is

not yet theoretically solid. There is a suggestion (Joe) that some predictions will be possible common to all these theories. (And even some specific

suggestions for such predictions were raised.) There is also a suggestion/hope (T) that most of the 10^** possible theories will be disqualified based on contradictory physics consequences. In any case, the fact that the damaging evidence was discovered by string theorists themselves speaks for the integrity of the ST endeavor.

Gina,

You’re adding nothing to the discussion here, just repeating in garbled form what others who do understand the issues have written. In particular, Joe does not claim to have predictions common to all theories, he was discussing something that is a feature of one class of compactifications but not others. Please stop adding to the noise level here.

I am just an intermediate grad student, but I agree with Gina.

As far as I can tell, the situation is: there are “old” string theorists

who are stuck in 1985 and hope the whole thing will go away;

more modern string theorists who realize this is a real issue with

the whole theory (but the theory may well still be correct and one

has to deal with the issue); and finally a bunch of people like

Peter and Smolin who really dislike string theory, for reasons you

can judge yourself (they don’t seem very sound to me). Anyway

I need to read my next review now (about supersymmetry), so

I’ll sign off.

Hi anonymous,

Before you run away, I am just curious why do you want enter a research field which is in the state of crisis, at least according to some “old” people. For 20 years, these old people led the pack, and only a handful of younger people (like Kachru) made a real impact (Douglas is still an older generation). What do you expect to learn? If you take landscape seriously, ST is no longer a TOE, so it doesn’t seem to contain this “romantic” flavor of fundamental theory that brought in the previous generations of students. I am also curious what is your advisor’s point of view.

I think taken in the best light, where we assume some of the strongest claims for what has been so far achieved, one would have to argue that string theory was a theory of properties of a final theory but I think it seems a bit unreasonable to claim there is anything that will force uniqueness … am I right?

I think the stuff about all possible universes having to exist just because the equations say so seems… dumb … that’s like saying because we can define all possible humans using DNA sequences then all possible humans exist …

The other issue is, that one can never be sure that one has discovered all the possible restrictions …

It’s an assumption (and a silly one at that) that there must be a direct correspondence between the universes being studied and actual universes …

Jean-Paul:

I talked to many people, and it seems the people who entered

the field in the 80s and 90s (before say 1996) all felt strongly discouraged from doing so (apparently the senior theorists at Harvard openly ridiculed the theory in the late 1980s). I feel now, maybe, like they did then: there is criticism of this theory, but it is based on irrational factors. The theory unifies gravity and quantum mechanics. Given that inflation occurs, any theory with many vacua will have the landscape issue to deal with. And it is hard to imagine a theory with a unique vacuum giving our bizarre word (even grand unified theories have many vacua). Maybe I’m wrong. We’ll see.

possibly adding to the ‘noise level’ here, I pose the question if ‘flux compactification’ has actually a rigorous mathematical background and if so if this would fit into a yet-to-be-established picture of mirror symmetry, for instance: is there an algebraic counterpart of ‘flux compactification’ in Kontsevichs picture or what could it be? Furthermore, I wonder if ‘monodromy’-questions are involved in questions of ‘fluxes’, families of Calabi-Yau manifolds being topologically trivial but symplectically nontrivial etc. or related questions of stability of special lagrangians in families. If someone knows a reference relating mathematical and physical research in these respects I would be thankful.