Why I am REALLY disappointed about string theory

[suprised]

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

No I wasn't listing generally known open problems, rather views that were, or still are, taken for granted by many, often leading to a lamp-post kind of research. That is, one looks at isolated spots where there is light, with the justification that one cannot see in the dark. But instead of trying to generate new light, most research was/is focused at the old light spots, investing an enormous amount of work to understand every detail there. There is nothing wrong with this per se, but I fear that many people implicitly believe that all there is are those light spots, and that their toy models can describe real nature if they were just lucky in finding the "right" model. That's why still after so many years still even more string vacua are constructed all the time, supergravity solutions found etc etc, despite that it is very unlikely that fundamentally important progress could be made in this way.

Certainly not all research is like that, eg the AdS/CFT correspondence is an example where a new floodlight had been switched on.

This list was quickly typed in without any particular order and certainly one could add more points, so that's in no way complete.

 

[suprised]

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?

These are just "extra" matter degrees of freedom, their presence being necessary for consistency. That for very special values of parameters these degrees of freedom may be interpretable in terms of compactified dimensions is "nice" and interesting, but not fundamentally important; one way so see this is to realize is that often a particular theory has multiple different higher dimensional interpretations (eg in terms of compactified heterotic or type UU strings), which just means that there is no objective, unambiguous reality of these compactification geometries. Therefore using this language creates a bias that can be very misleading.

For example, as said, the belief that realistic string models describing our world should be thought of in terms of a two-stage processs, namely 1) compactification on a CY to four dimensions and 2) breaking of N=1 Susy, is very much motivated by the naive compactification picture. But coming from a different perspective, say from a world-sheet perspective with nongeometrical degrees of freedom, such a szenario would seem quite unnatural/implausible.

 

[fzero]

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.

Well 15-20 years ago string theorists were realizing that it was probably very important to understand nonperturbative physics as well. See for example Banks and Dine "Coping With Strongly Coupled String Theory," http://arxiv.org/abs/hep-th/9406132 The contact with nonperturbative physics through dualities that were discovered around the same time was a primary draw. For the most part, these dualities involve fixed backgrounds, though many of them do involve topology change.

As for fixing a geometric background, it is not always a drawback, especially if the interest is in computing low-energy physics. I don't think that anyone would disagree that we would want to be able to compute SM parameters in a fixed model. It's not obvious that having a background independent formalism would make this easier, though there could be surprises. More likely would be that any new piece of wisdom about nonperturbative computations would shed more light here. In any case, it would not really be advantageous to completely drop the study of fixed backgrounds.

As for nongeometric models, I have a different view from surprised. It is part of the lore that, at least for models with 4d SUSY, every nongeometric critical theory is equivalent to a CY compactification at some special value of moduli. This goes under the name of Gepner models and it is not something that I have studied in sufficient detail to do justice to, either in explanation or in citing the most definitive references. Nevertheless, I don't think that this is accidental and is probably tied to a deep universality of string backgrounds that we should hope to understand. I understand noncritical strings to an even smaller degree, but I think that if there is some underlying selection mechanism, those would be a starting point to find it.

Now background dependence is very important for understanding quantum gravity, as I've agreed before. Such a formalism would hopefully lead to further distinction between different backgrounds, but as I've suggested above, probably would not directly lead to a better understanding of low-energy properties.

 

[marcus]

These are just "extra" matter degrees of freedom, their presence being necessary for consistency. That for very special values of parameters these degrees of freedom may be interpretable in terms of compactified dimensions is "nice" and interesting, but not fundamentally important;...

Excellent, thanks much!

...
As for fixing a geometric background, it is not always a drawback, especially if the interest is in computing low-energy physics. I don't think that anyone would disagree that we would want to be able to compute SM parameters in a fixed model. It's not obvious that having a background independent formalism would make this easier, though there could be surprises. More likely would be that any new piece of wisdom about nonperturbative computations would shed more light here. In any case, it would not really be advantageous to completely drop the study of fixed backgrounds...

Now background dependence is very important for understanding quantum gravity, as I've agreed before. Such a formalism would hopefully lead to further distinction between different backgrounds, but as I've suggested above, probably would not directly lead to a better understanding of low-energy properties.

fzero I can't argue with what you say here. It seems to be a reasonable question to ask "what could a background independent QFT be good for?" The only answer seems to be that it might extend understanding into a couple of regimes of extreme density (BB and BH) Perhaps not even BH since we may never witness a BH evaporate and so any theory not comparable to observation would seem vacuous. But at least hopefully BB. You make a commonsense point that one wants to keep studying QFT etc on fixed geometric backgrounds. Certainly. I don't have the time right now to try to say something nontrivial in response (and not sure I could anyway, maybe someone else will respond.)

AFTERTHOUGHT: I think what you mean by "the study of fixed backgrounds" is fields etc on manifolds-with-fixed-metric. The gnawing question is why bother going to, say, manifoldless? I confess that one thing I like about Rovelli's program ("how to formulate a background independent QFT") is the mathematical challenge.

I think it is very hard to replace, with something comparably simpleandbeautiful, Riemann's 1850 setup of a manifold-with-fixed-metric (it is such an obviously good setup!). I think, this will seem quixotic, challenges of that order are good for us. They can lead to stuff.

Compared with that, merely extending our understanding to cover the BB, and maybe BH, seems like just the icing on the cake. Just trimmings.

I would really like to see Riemann's 1850 continuum invention superseded. For essentially mathematical reasons. So much for confessions.

 

[marcus]

Since we just turned a page, I will recopy Suprise's list of 8 points from post #523 which seems to have fertile material for discussion, plus for completeness I will add his later clarification on the previous page.

[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...

This clarification is in response to a question by Tom Stoer.

No I wasn't listing generally known open problems, rather views that were, or still are, taken for granted by many, often leading to a lamp-post kind of research. That is, one looks at isolated spots where there is light, with the justification that one cannot see in the dark. But instead of trying to generate new light, most research was/is focused at the old light spots, investing an enormous amount of work to understand every detail there. There is nothing wrong with this per se, but I fear that many people implicitly believe that all there is are those light spots, and that their toy models can describe real nature if they were just lucky in finding the "right" model. That's why still after so many years still even more string vacua are constructed all the time, supergravity solutions found etc etc, despite that it is very unlikely that fundamentally important progress could be made in this way.

Certainly not all research is like that, eg the AdS/CFT correspondence is an example where a new floodlight had been switched on.

This list was quickly typed in without any particular order and certainly one could add more points, so that's in no way complete.

 

[ApplePion]

<<As far as I can see string theory (whatever this means - ST, F-, M-, ...) is the only candidate with the potential to unify all interactions including gravity.>>

Maybe the correct theory is not yet a "candidate". I suspect you are tacitly assuming that whatever the correct theory is is something currently on the table.

 

[Fra]

These are just "extra" matter degrees of freedom, their presence being necessary for consistency. That for very special values of parameters these degrees of freedom may be interpretable in terms of compactified dimensions is "nice" and interesting, but not fundamentally important;
...
Therefore using this language creates a bias that can be very misleading.

I like the direction you say here.

Essentially I take it you mean that understanding string theory should try to release itself from the geometric abstractions.

Assume we do so, then how do we think of the starting points, like the string action. I mean, supposed we try to release ourselves from the geometric interpretation... of both kinematics and dynamics, then what other abstraction can be used to MOTIVATE and understand say the string action?

In particular, what does even a "string" means? I mean, if it's not thought of in the geometrical sense of a oscillating string. Then what is it? ;-)

/Fredrik

 

[arivero]

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
.

It remembers me to the first reaction a student has when s/he is introduced to General Relativity curvature: that it must be curved somewhere, and then it should imply the existence of a hyperspace to embed it. So for a naive student, General Relativity predict at least 2*4+1 space-time. Worse, it one looks to embedding theorems for metrics of Lorentzian signature, it goes up to dimension 90 or so. But fortunately the GR practicioners inmmediately notice how irrelevant the embedding is, and we are never told about such dimensions as physical. Actually, even the embedding theorem is not mentioned, except if you go to view some film about Nash :-)

- That strings predict susy, or have an intrinsic relation to it (in space-time)

This is the only one where I beg to differ (the mass of electrons or muons, I agree that it is not fundamental, while I still think it is going to be calculable at the end). As a crackpot, I believe I know about a 90% of the final answer, and susy is still a basic piece here, and strings need susy as heavily that it is impossible to think that it is not an intrinsic thing. The decomposition $$496=2^4 (2^5-1)$$ should have an explanation using strings and susy, and the same then would apply to $$6=2^1 (2^2-1)$$, the numer -according my papers- of identically charged squarks (six of down type and charge red, six of up type and charge red, six of down type and charge blue, etc etc)

 

[marcus]

As a crackpot, I believe I know about a 90% of the final answer, and susy is still a basic piece...

Nature herself may smile on crackpots of your kind, if so you be, Alejandro.

 

[Calrid]

<<As far as I can see string theory (whatever this means - ST, F-, M-, ...) is the only candidate with the potential to unify all interactions including gravity.>>

Maybe the correct theory is not yet a "candidate". I suspect you are tacitly assuming that whatever the correct theory is is something currently on the table.

This is also actually a fallacy. The standard model has the potential to unify all the interactions not to mention LQG. Just because as yet it hasn't been able to do so does not mean it can not. String theory hasn't been able to make itself testable, it is something that may in fact never be testable. It's another piece of propaganda put about that isn't even remotely true.

 

[Haelfix]

That for very special values of parameters these degrees of freedom may be interpretable in terms of compactified dimensions is "nice" and interesting, but not fundamentally important; one way so see this is to realize is that often a particular theory has multiple different higher dimensional interpretations (eg in terms of compactified heterotic or type UU strings), which just means that there is no objective, unambiguous reality of these compactification geometries. Therefore using this language creates a bias that can be very misleading.

A lot of string theorists in our theory group share this point of view. I must say I am a bit uneasy with this, although I sympathize in the sense that many theories have several different mathematical interpretations. Eg you can treat GR as a nongeometric theory and do just fine. Likewise you can of course view supersymmetry as a sort of generalized manifold with infinitesimal 'fermionic' extra dimensions and its just a matter of convenience which description one uses.

However like it or not, we do live in a 4 dimensional world, with very large macroscopic scale dimensions and at least to me it is useful to perceive of the world in this way, rather than mix everything up in a sort of gigantic quantum soup where even simple rods and rulers no longer make sense.

Marcus asked why a manifold is important? Well we know there has to be one at some scale, b/c gravity is a long range force and the equivalence principle must hold to very high accuracy. Further any theory of quantum gravity must become semiclassical rather rapidly and smooth out all the decidedly quantum modes lest it be falsified experimentally.

Anyway, my issue with Gepner models is they seem to have issues generating correct family structures in the standard model, which is to be contrasted with some of the other vacua that seem to pick out 3 generations uniquely. Further it is unclear which way the generalization goes. I distinctly recall a theory seminar where it was shown that Gepner models typically reproduce isolated points in the moduli space arising from usual CY compactifications. Consequently it was perhaps the case that the nongeometric vacua were subsets of the geometric ones..

edit: for non string theory cognescenti.. Gepner models naively seem to generalize world sheet coordinates. Instead of scalar fields, we are thinking about more abstract mathematical objects like Ising models or conformal minimal models and things like that. They are rather weird in that you have states with fractional charges floating around the place. However, surprisingly you can prove the equivalency of these models with the more familiar ones (eg ones with the usual boson and fermion degrees of freedoms) by analyzing how objects behave in the target space. Here the actual dimensionality of the critical string is completely obscured, although other physical criteria (like recuperating supersymmetry) becomes manifest. The surprising thing here is that what started out as an apparent generalization from the worldsheet point of view, actually becomes equivalent or even perhaps weaker looking at the target space.

 

[Physics Monkey]

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.

I like this list, and the ensuing discussion. Since you didn't specify the current state of thinking, may I ask your opinion about it? For example, would a majority of string theorists disagree with: string theory is a rich theory, with a landscape of solutions where to 0th order anything goes, where susy is not essential or generic and where higher dimensional geometry is not essential or generic?

I also wonder about the following, instead of asking what can be realized in string theory, perhaps its better to ask what can't be realized in string theory? I have in mind the recent work in 6d demonstrating that essentially all low energy theories of a certain type are either inconsistent or descend from string theory.

 

[smoit]

With regard to space-time SUSY, as I understand, compactifications on backgrounds that break all supersymmetries, as opposed to, say, CY compactifications where N=1 SUSY is preserved, typically lead to tachyons in the string spectrum, which indicates an instability. There is a very beautiful paper by Adams, Polchinski and Silverstein where they show that a non-SUSY orbifold compactification containing tachyons in the twisted sector undergoes tachyon condensation that drives this non-SUSY configuration to a supersymmetric one.

http://arxiv.org/abs/hep-th/0108075

I think that this phenomenon is not unique to orbifolds and partially justifies an assumption that one needs to consider compactifications on backgrounds that preserve SUSY in 4D.

Another thing that I find particularly remarkable about CY or G2 holonomy compactifications is that these highly curved and extremely complicated spaces are, in fact, Ricci flat $$R_{mn}=0$$, so one needs no elaborate sources to support the metric! Of course, one needs to still stabilize the moduli without breaking the CY condition but this is now more or less understood, see e.g. http://arxiv.org/abs/1102.0011 .

 

[fzero]

I like this list, and the ensuing discussion. Since you didn't specify the current state of thinking, may I ask your opinion about it? For example, would a majority of string theorists disagree with: string theory is a rich theory, with a landscape of solutions where to 0th order anything goes, where susy is not essential or generic and where higher dimensional geometry is not essential or generic?

There are several constraints on consistent string theories. As smoit points out, absence of SUSY typically leads to tachyons. In the usual consideration of a flat Lorentizan background, worldsheet SUSY is used to construct the GSO projection that removes the normal closed string tachyon. The resulting spectrum still has the massless spin 3/2 gravitino. Consistent quantization of such a field requires spacetime supersymmetry as a gauge symmetry, in analogy with the way massless spin 1 requires ordinary gauge invariance. So it is this requirement that results in the statement that string theory predicts SUSY. A phenomenological question is at what scale SUSY is spontaneously broken.

As I and Haelfix pointed out, the nongeometric models are connected to geometric models, so it is not clear that much is gained by changing any focus away from geometry. It may still be that interpreting the internal dimensions as true dimensions of spacetime is not necessary, but it remains convenient for many reasons.

People often speculate whether there is a new set of degrees of freedom that could be used to describe strings nonperturbatively. The BFSS matrix model and AdS/CFT both provide such new degrees of freedom in particular backgrounds and limits. In AdS/CFT the gauge degrees of freedom are not geometric at all in the standard sense.

There are further objections to "anything goes" contained in Vafa's swampland paper, http://arxiv.org/abs/hep-th/0509212, which led in later work to the conclusion that gravity should always be the weakest force in string theory http://arxiv.org/abs/hep-th/0601001

There are other bits of lore, such as all global symmetries must descend from gauge symmetries.

I also wonder about the following, instead of asking what can be realized in string theory, perhaps its better to ask what can't be realized in string theory? I have in mind the recent work in 6d demonstrating that essentially all low energy theories of a certain type are either inconsistent or descend from string theory.

I wouldn't say better, I would say that people should be working on both sides. As evidenced by the literature, people like Vafa and Taylor are working on this, so it's getting the right sort of attention.

 

[arivero]

Nature herself may smile on crackpots of your kind, if so you be, Alejandro.

Lets wait to see if Nature is kind enough to show us the fermionic partners. Massive gluinos and photinos at LHC scale, that should be a real bless.

 

[suprised]

I have two comments for the time being:

1) Whether SUSY is needed for consistency of strings. I don't believe, nor I hope so. Our world is not SUSY at low energies, we don't see a tachyon, so strings better are able to cope, as a matter of consistency, with non-susy backgrounds. And if they could cope with that, why should be SUSY then need to be restored at the weak scale and not, say, right at the Planck scale?

Indeed SUSY is a powerful symmetry principle that helps to prevent tachyons, and protect the cc etc; generically models without SUSY are threatened by tachyonic instabilities. And of course SUSY is very handy for heaving treatable models, but that's not an argument why Nature should care about this. AFAIK there is no theorem that says, non-susy strings imply tachyons (and as said above, there better be no such theorem). Thus it is unclear whether SUSY is a technical convenience for toy model building, or really a deep principle of nature.

The situation is in fact more complicated, as there exist metastable vacua where SUSY is "broken temporarily" and the true ground state is SUSY. AFAIK no definite conclusions can be drawn here, all I want to say is that the scenario of having unbroken SUSY at low energies may have been quite a substantial blind ally.

2) Geometrical vs non-geometrical compactifications. With geometrical I meant "classical geometry" involving manifolds, field configurations like vector bundles, etc. In short, all what comprises the good old supergravity school of thinking. Certainly this has been very useful and fruitful, but neverless captures only the boundary of the string parameter space.

With non-geometrical I meant "stringy geometry". I make my life easy and define this by simply saying that's it is a kind of generalized geometry that takes stringy features properly into account (eg by identifying classical geometries that are related by dualities). It is eg well-known that the notion of D-branes wrapping sub-manifolds needs to be replaced by abstract mathematical constructs like derived categories of coherent sheaves, when we move away from the boundary of parameter space). This would be the proper language to describe strings in the bulk of their parameter space. And generically this can NOT be mapped back, by dualities, so some classical geometry.

Again, all what I want to say is that focusing on the language of classical geometry, can be a major blind ally since it excludes the _main part_ of the string parameter space.

 

[suprised]

Since you didn't specify the current state of thinking, may I ask your opinion about it? For example, would a majority of string theorists disagree with: string theory is a rich theory, with a landscape of solutions where to 0th order anything goes, where susy is not essential or generic and where higher dimensional geometry is not essential or generic?

Well that depends to whom you talk to. I believe the majority of colleagues would say that SUSY and naive extra dimensional geometry are essential, not only technically. I raise these points here as a Devil's advocate since Tom asked for potential blind allys.

 

[suprised]

Anyway, my issue with Gepner models is they seem to have issues generating correct family structures in the standard model, which is to be contrasted with some of the other vacua that seem to pick out 3 generations uniquely. Further it is unclear which way the generalization goes. I distinctly recall a theory seminar where it was shown that Gepner models typically reproduce isolated points in the moduli space arising from usual CY compactifications. Consequently it was perhaps the case that the nongeometric vacua were subsets of the geometric ones..

edit: for non string theory cognescenti.. Gepner models naively seem to generalize world sheet coordinates. Instead of scalar fields, we are thinking about more abstract mathematical objects like Ising models or conformal minimal models and things like that. They are rather weird in that you have states with fractional charges floating around the place. However, surprisingly you can prove the equivalency of these models with the more familiar ones (eg ones with the usual boson and fermion degrees of freedoms) by analyzing how objects behave in the target space. Here the actual dimensionality of the critical string is completely obscured, although other physical criteria (like recuperating supersymmetry) becomes manifest. The surprising thing here is that what started out as an apparent generalization from the worldsheet point of view, actually becomes equivalent or even perhaps weaker looking at the target space.

Gepner models illustrate my points. Some of these models have a direct relation to string compactifications in CY spaces (in the deep quantum regime, ie, where the CYs are very small and string effects are important).

The prime example is the quintic, described by a Gepner model with Landau-Ginzburg superpotential

W = Sum_(i=1)^5 (x_i)^5

W=0 is nothing but the equation of the quintic CY:
5 coordinates minus the equation W=0, minus rescaling gives 3 (complex) coordinates, so this yields indeed a six real-dimensional CY. So here we can make a nice map between 2d CFT and space-time compactification manifold.

The following Gepner model is from the 2d CFT point of view on the same footing as the model before:

W = Sum_(i=1)^9 (x_i)^3

However, 9 coordinates minus the equation W=0, minus rescaling gives 7 (complex) coordinates... so this looks naively like a 14 dimensional manifold... as such certainly not useable as compactification manifold! But this model defines a perfectly valid string vacuum.

So we see here that the 2d, "non-geometrical" formulation gives rise to more string vacua than most would have thought of when naively thinking about compactification manifolds!

 

[atyy]

Since the extra parameters are not necessarily spacetime dimensions, are there any examples where these parameters give rise to 4D spacetime and the rest being non-geometrical?

 

[fzero]

Since the extra parameters are not necessarily spacetime dimensions, are there any examples where these parameters give rise to 4D spacetime and the rest being non-geometrical?

Yes, the restrictions on matter in the superstring come from requiring worldsheet conformal invariance. The anomaly is proportional to the total central charge, c, of the worldsheet theory. One first computes the central charge of the ghosts required to fix worldsheet diffeomorphism and Weyl invariance. This is the $$b,c$$ system and has central charge -26. If we don't include worldsheet SUSY, then the worldsheet matter must have c=26. Since a free boson CFT has central charge 1, this leads to the result that D=26 for the bosonic string.

If we include SUSY, we find another ghost system $$\beta,\gamma$$ that fixes local worldsheet SUSY. This system contributes another central charge +11, leaving -15. A free fermion has central charge 1/2, so 15 = 10(1+1/2) gives D=10 for the usual superstring.

If we want only a 4D system, we will be left with central charge -15+4(1+1/2) = -9, so our not-necessarily-geometric "internal" CFT must have central charge c=9. In the geometric compactifications, this is supplied by 6 more boson-fermion pairs, but in general could be supplied by any CFT we can stitch together.

 

[suprised]

Since the extra parameters are not necessarily spacetime dimensions, are there any examples where these parameters give rise to 4D spacetime and the rest being non-geometrical?

Zillions of examples...

 

[arivero]

1) Whether SUSY is needed for consistency of strings. I don't believe, nor I hope so. Our world is not SUSY at low energies,

This is the blindness -the wrong turn- I try to fight in the last years: our world IS susy at low energies, and because of it we confused the pion with the muon in the fifties.

It was a very prepostereous thing to say, so five minutes after proposing it (basically a couple of publications by John H. Schwarz in 1971, following the discovery of the Ramond string), everyone, including Schwarz, forgot about it. But with three generations, the degrees of freedom match. It is susy, it is the qcd string, they were right from the start, and the only point today is why the non-chiral interactions get their gauge bosons massless, but not the partners. If we find the gauginos -and only them- the question will be settled.

 

[tom.stoer]

oops :-[

Could you please write down how to "pair" the known particles?

 

[atyy]

Yes, the restrictions on matter in the superstring come from requiring worldsheet conformal invariance. The anomaly is proportional to the total central charge, c, of the worldsheet theory. One first computes the central charge of the ghosts required to fix worldsheet diffeomorphism and Weyl invariance. This is the $$b,c$$ system and has central charge -26. If we don't include worldsheet SUSY, then the worldsheet matter must have c=26. Since a free boson CFT has central charge 1, this leads to the result that D=26 for the bosonic string.

If we include SUSY, we find another ghost system $$\beta,\gamma$$ that fixes local worldsheet SUSY. This system contributes another central charge +11, leaving -15. A free fermion has central charge 1/2, so 15 = 10(1+1/2) gives D=10 for the usual superstring.

If we want only a 4D system, we will be left with central charge -15+4(1+1/2) = -9, so our not-necessarily-geometric "internal" CFT must have central charge c=9. In the geometric compactifications, this is supplied by 6 more boson-fermion pairs, but in general could be supplied by any CFT we can stitch together.

Zillions of examples...

So we don't obviously need Calabi-Yau compactifications?

 

[arivero]

oops :-[

Could you please write down how to "pair" the known particles?

Sigh . Guys, just look at the data.

It is about taking seriously the ideas of http://dx.doi.org/10.1016/0370-2693(71)90028-1" ): the fermion in the dual model is susy to gluonic strings. So now all you need is to terminate the gluonic string. Regretly in 1971 there were only three states available to terminate the string: u, d, and s. Now we have the full history, and the experimental data tell us that we can terminate the gluonic string with five and only five different states: u, d, s, c, b.

So just count, please, just do the SU(5) global flavour game, and count. How many states do you get of charge +1? six, by terminating with particle and antiparticle. How many of charge +2/3? six of each colour, by terminating with an antiparticle at each end of the string. How many of -1/3? six. How many +1/3, -1, -2/3? Same: six, six, six. And how many neutrals? of course, twelve: the other half of the 24 of SU(5).

BONUS: Does it means that string theory, given as input the 3-2-1 gauge theory of the SM, predicts three generations? No exactly; only if we require that the neutral leptons must be produced too. If we only look at the quark sector, then any pairing of $2^{p}$ "up quarks" with $2^{p+1} -1$ "down quarks" will produce equal number, $2^p (2^{p+1} -1)$ of up and down combinations, and p=1 is just the simplest case. Numerically minded people will notice that p=4 amounts to 496, but a theory with 16 light "down" quarks, 31 light "up" quarks and a total of 248 generations seems not to be the object that Nature has offered us.

EDIT: other references using "fermion-meson": http://dx.doi.org/10.1016/0550-3213(74)90529-X Nuclear Physics B Volume 74, Issue 2, 25 May 1974, Pages 321-342 L. Brink and D. B. Fairlie; http://www.slac.stanford.edu/spires/find/hep/www?j=NUCIA,A11,749 Nuovo Cim.A11:749-773, 1972 by Edward Corrigan and David I. Olive. Modernly, they are some works, in the framework of SQCD and also in Holography, that work with "mesinos", in the sense of susy partners of mesons. But note that phenomenologists call also "mesino" to the combination of squark and quark.

 

[fzero]

So we don't obviously need Calabi-Yau compactifications?

I wouldn't say don't need, for a couple of reasons. For one, CY compactifications are a class of c=9 theories. However, it could be that a nongeometric model gives physics that is close to reality. As an example, there are some models with 3 generations in http://arxiv.org/abs/1009.1320 though they also seem to find massless fractionally charged states that could be a problem for phenomenology.

However, it is known that many of these nongeometric theories are equivalent to CY compactifications at special points in moduli space. For some evidence of this, one can look at Witten's http://arxiv.org/abs/hep-th/9304026, which relates some of them (so called $$N=2$$ minimal models) to Landau-Ginzburg theories. These LG theories are themselves known to be a phase of CY sigma models http://arxiv.org/abs/hep-th/9301042

I don't believe that the state of knowledge about the equivalence between nongeometric and geometric models is developed completely, but I think it's strong enough that it wouldn't make sense to drop CY models. If anything, the equivalence itself should be studied further, since it might teach us more things about the space of c=9 models.

 

[tom.stoer]

I would like to come back to suprised's list regarding possibly wrong turns.

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

Let's look at this list again: there is a deep connection between some topics; that's why I was mentioning background independence. I would like to comment on this once more.

String theory walked - for a rather long time - on the trail of particle physics and quantum field theory. Of course there was a graviton, but after recognizing this particle one immediately focussed on QFT-like reasoning (background, strings on top of this background, perturbative quantization, ...). I would say that the first few topics are essentially due to this perception of string theory.

Looking at the field today most researchers are convinced that non-perturbative approaches are required. Thousands of backgrounds / vacua have been identified, but still they are mostly perceived as reasonable backgrounds on which standard particle- or QFT-like theories can be formulated. This is OK for model building an phenomenology (it is not only OK but of course heavily required in order to achieve a closer relation to reality).

But using intuition to find such backgrounds and doing "ordinary physics" on top of these backgrounds does not help in order to understand the relation between these backgrounds and to identify the "unique" and deeper origin of these backgrounds, which I would call the underlying theory.

I think another wrong turn - perhaps the most serious one - would be to turn a bug (the missing unique underlying theory) into a feature (we do not need a unique underlying theory). It would be same as looking at the periodic system and stating that happily there is no underlying theory required as we have a collection of relations between different chemical elements.

I think we do not need to look for a selection principle ("why is it iron instead of copper?"), we do not need to condemn the landscape ("iron, copper, mercury, oxigen, ... is too much; we need a single solution"), we do not need to look for a way to calculate the mass of the electron ("how do we calculate the mass of the mercury atom in a theory which does not explain why there is a mercury atom?"). All what we have to do is to understand what string theory really is. My impression is that we still do not know, we are scratching at the surface, we see some "effective models", not more (and not less).

So 1. - 4. may have been wrong turns - but were overcome somehow over the last years. 5., 6. and 8. are perhaps wrong turns which are in the spotlight today. 7. is not a wrong turn but the essential driving force of progress in physics. I would not abandon it w/o having a worthy successor.

I am still with David Gross (and others - like Weinberg I guess) who asked exactly these questions:

• WHAT IS STRING THEORY?
  This is a strange question since we clearly know what string theory is to the extent that we can construct the theory and calculate some of its properties. However our construction of the theory has proceeded in an ad hoc fashion, often producing, for apparently mysterious reasons, structures that appear miraculous. It is evident that we are far from fully understanding the deep symmetries and physical principles that must underlie these theories. It is hoped that the recent efforts to construct covariant second quantized string field theories will shed light on this crucial question.
  
• We still do not understand what string theory is.
  We do not have a formulation of the dynamical principle behind ST. All we have is a vast array of dual formulations, most of which are defined by methods for constructing consistent semiclassical (perturbative) expansions about a given background (classical solution).
  
• What is the fundamental formulation of string theory?

Denying the relevance of these questions is - in my opinion - the "wrongest turn ever".

 

[suprised]

Nicely said, Tom.

Though I think I should explain what I meant with 7) "there exists a unique underlying theory".
Much could be said here. For the time being, let me provocative and say the following:

Strings seem to be the natural generalization of gauge theory, actually closely related to it by dualities, such as AdS/CFT; in the latter context, strings are indeed reconstructed from gauge theory. So let's view strings as analogous to gauge theory; and then re-ask the same question: "what is the underlying unique theory of gauge theory" ?

Clearly this is a not very fruitful question to ask, because it presupposes something which does not exist, at least in the sense of the question. All there is with gauge theory, are various degreses of freedom that are exposed depending on the energy scale (gluons, quarks, mesons...)

As for strings, the situation is unclear but it may be similar - there may be no further "unique underlying theory". All there might be is the complicated web of perturbative approximations related by dualities, but there is no regime where "universal, more fundamental" degrees of freedom would be liberated.

The real question is whether there is an encompassing, "off-shell" mother theory which would contain all the known theories as "critical points", and describe transitions between them, etc. This may, or may not exist (analogous to gauge theory). So this question is a potential blind ally as well!

 

[suprised]

So we don't obviously need Calabi-Yau compactifications?

They are just special examples of vacua, their main advantage is being relatively well under technical control. That's why there has been so much focus on them, unfortunately thereby creating the impression that they would be somehow essential. But there are zillions of other constructions (generalized geometries with fluxes, non-geometric vacua, brane backgrounds, non-perturbative F-theory vacua, M-Theory vacua,... ).

Of course, many of such vacua are equivalent via dualities, and this shows, again, that there is no objective, unambiguous meaning of a compactification geometry.

 

[Fra]

our construction of the theory has proceeded in an ad hoc fashion, often producing, for apparently mysterious reasons, structures that appear miraculous. It is evident that we are far from fully understanding the deep symmetries and physical principles that must underlie these theories.

This is the most serious concern I've always had.

Exactly becuase, string theory seems to be a framework or research program - rather than a unique mature theory, the logic of reasoning used is even more important; because this is what defines the program.

/Fredrik

 

[tom.stoer]

... let's view strings as analogous to gauge theory; and then re-ask the same question: "what is the underlying unique theory of gauge theory" ?

Clearly this is a not very fruitful question to ask, because it presupposes something which does not exist, at least in the sense of the question. All there is with gauge theory, are various degreses of freedom that are exposed depending on the energy scale (gluons, quarks, mesons...)

As for strings, the situation is unclear but it may be similar - there may be no further "unique underlying theory". All there might be is the complicated web of perturbative approximations related by dualities, but there is no regime where "universal, more fundamental" degrees of freedom would be liberated.

The real question is whether there is an encompassing, "off-shell" mother theory which would contain all the known theories as "critical points", and describe transitions between them, etc. This may, or may not exist (analogous to gauge theory). So this question is a potential blind ally as well!

I agree to this view - at least currently string theory seems to be a framework for constructing and defining theories; this framework is capable of producing ordinary (SUSY) gauge theory plus gravity (which is not possible in the framework of gauge theory alone).

But already in gauge theory we asked the question "why the standad model? why exactly U(1)*SU(2)*SU(3)"? Or "why gauge bosons, why not spin 5/2 particles, ...?"

I agree that these questions (translated to the string theory language) could be dead ends. But I bet that going into these directions we will learn a lot - even if they are dead ends.

 

[arivero]

BONUS: Does it means that string theory, given as input the 3-2-1 gauge theory of the SM, predicts three generations? No exactly; only if we require that the neutral leptons must be produced too. If we only look at the quark sector, then any pairing of $2^{p}$ "up quarks" with $2^{p+1} -1$ "down quarks" will produce equal number, $2^p (2^{p+1} -1)$ of up and down combinations, and p=1 is just the simplest case. Numerically minded people will notice that p=4 amounts to 496, but a theory with 16 light "down" quarks, 31 light "up" quarks and a total of 248 generations seems not to be the object that Nature has offered us.

Allow me a correction to this remark: Of course, the quark sector condition works for any integers $q$ and $2 q -1$, with $q$ an even number, not necessarily a power of two. But that the powers of two are an interesing subset was noted by Peter Crawley in other thread time ago and I am kind of obsessed with this, because it could constitute the way to reconnect with usual string models, via the above p=4 case.

 

[Fra]

Clearly this is a not very fruitful question to ask, because it presupposes something which does not exist, at least in the sense of the question. All there is with gauge theory, are various degreses of freedom that are exposed depending on the energy scale (gluons, quarks, mesons...)

Unique theory is a strong phrase, and I do not expect that either in the meaning of eternal objective theory.

But I think a fruitful and necessariy question seems to require an understanding of these "various degrees of freedom" and how and why they are related by means of gauge symmetries in the context of a measurement theory.

I expect that state spaces and theories are to be described as the result of an interaction history. This includes also inferred "gauge symmetries". That are like inferred evolving constrainst that constrain the action of the observer. It's interesting that these symmetries are "energy dependen" as you say, but one can also see them as generally observer dependent. All this is quite interesting and seems to lead to an intrinsic measurement theory that involved emergent constraints (gauge symmetries).

This MAY suggest a general framework for inference (this is exactly why there is no external FIXED unique description, since it keeps evolving)

The question I ask is: could string theory be that framework? If we can understand ratianally that the action of quantized strings in classical backgrounds somehow corresponds to such "gauge choices" that are furthermore scale dependent (so as to give rise to a range of dualities) then I think that would be extremely beautiful and powerful.

Ie. that vision is nice. But is really string theory this theory of theory that I think a lot of people that do not today enjoy string can appreciate?

For example, has any string theorist ever tried to justfiy the basic string action, from a pure inferencial perspective? Ie. that the string action can be understood as an optimal action on the set of possible changes constriaied by historically inferred constraints? (we are conceptual analogues of gauge symmetry)

I think that the focus and hope of string theory is to actually BE the "theory of theory" that some hopes for.

What traits would one ask for such type of theory, and what is the purpose of such theory? descriptive or as an interaction tool?

/Fredrik

 

[suprised]

Fra, I really can't answer your questions, I barely understand them.

But I comment on this:

For example, has any string theorist ever tried to justfiy the basic string action, from a pure inferencial perspective?

There is no such thing like a basic string action. There are various actions, with different symmetries (like heterotic string world sheet, like type II string world sheet, like open type I world sheet...). They are all different, and each one refers to some particular perturbative approximation centered at a different regime. Moreover, for F-theory or M-theory such "world-sheet" actions are not known or may not exist; as we have discussed earlier, there are quantum theories which are strongly coupled and no lagrangian or action description of them exists.

So the string world-sheet perspective (Polyakov action and generalizations), while very useful in many situations (eg see the above discussion about CFT and internal degrees of freedom), is hardly fundamental. Trying to find a deeper meaning of it had been another of many blind ally's.

That's one of the most important conceptional riddles: does a "fundamental" action that would universally describe strings in every corner of the parameter space exist at all? I don't know but I doubt it.

 

[Fra]

I know what I asked is fuzzy, but thanks for trying to answer.

There is no such thing like a basic string action. There are various actions, with different symmetries (like heterotic string world sheet, like type II string world sheet, like open type I world sheet...). They are all different, and each one refers to some particular perturbative approximation centered at a different regime. Moreover, for F-theory or M-theory such "world-sheet" actions are not known or may not exist; as we have discussed earlier, there are quantum theories which are strongly coupled and no lagrangian or action description of them exists.

So the string world-sheet perspective (Polyakov action and generalizations), while very useful in many situations (eg see the above discussion about CFT and internal degrees of freedom), is hardly fundamental. Trying to find a deeper meaning of it had been another of many blind ally's.

Yes there are different string actions dependong on what string theory you consider, but that doesn't avoid my question:

Since you might have figured from my strange comments that I'm slowly working on an inference perspective to physics, and in this context, one can talk about actions as a way to measure the information divergence of possible futures relative to present. The idea is to define expected change not as dynamics realtive to external time, but with respect to a observer dependent entropic flow. IE to understand the concepts w/o referencing mechanical or geometrical visualisations.

As far as I know (even though yes there are different string actions) the actions is understood at least originally simply from the CLASSICAL ACTION you would expect from a litterally oscillating string. Then this is put in a background and you quantize etc.

The reason what I keep asking this because I sincerely think that there IS a deeper way to understand strings (or a way to at least connect string theory to something else). But this would require a deeper understanding of string actions and background beyond the classical geometric "picture" it started out as.

Maybe this is included in the open issue you already defined, but the basic string itself and the string action is a good starting point.

That's one of the most important conceptional riddles: does a "fundamental" action that would universally describe strings in every corner of the parameter space exist at all? I don't know but I doubt it.

I don't think so either it wasn't what I meant.

I meant that you can only "measure" one theory with respect to another one; by including a renormalized version of the first in the second one in a holographic sense.

But maybe we can in this way understand how theories interact. If I understand you, you also seek a way to understand how say transitions between different theories work, right?

What I am suggesting, and that does connect to the question I asked about the meaning of string actions, is that instead of thinkg in terms of a gigantic state space where you have transitions between theories, maybe the better way is to think of the "transitions" in terms of INTERACTING theories, that are negotiating.

Ie. the transitions are then simply internal revision in the light of new information. There is a good change to connect then the understanding of a string (seen as a simple measure on it's environment) to the foundations of measurement theory.

This means that the "background of the string" is defined by the interaction context (ie. neighbouring strings). But the difference is that, this "background space" only exists from the point of view of the string itself.

Ie if we thinkg of a string as an observer! then the string can "as far as it cna infer" conlude that it lives in this background space, and thus the rational action of the string (defined in the way I SEEK in the original question) is then merely doing a random walk in this effective background.

Transitions from different string theories would then (maybe?) correspong to the string observer remapping it's internal structure, so that giving instnatly "consistent" expectations, it becomes more stable.

What comes to my mind first is to tro "reproduce" or connect the ordinary string actions to some probabilistic measure based on permutations of string configurations - assuming ou can count it, maybe starting with discrete strings?

If such a deeper understanding of the string, and the string action as observers resp rational actions, I think it would be a major boost and it would help solve many questions. It would also force a new way of thinking about this.

Totally relased from the simple "geometrical pictures" you also mention you want to loose.

So the question is, what do we replace that with? I propose the inferentical perspective, but the connection to string seems to be in sight, but yet I'm not sure of anyone works in this direction.

Edit: Thinking in the direction is this http://math.ucr.edu/home/baez/nth_quantization.html. This is related to probabilities of probabilities which in turn related to renormalization of theories.

Could be generate string from something else, that does not come with the ad hoc or classical pictures to it? Something purely inferential?

/Fredrik