Why I am REALLY disappointed about string theory

[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

 

[marcus]

FOR CONTINUITY since we're on a new page, it may help to carry over some essential posts. This of Suprised was seminal:

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:
...

Tom's most recent long one was:

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

===quote post #554 ===
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".
==endquote from Tom's post #554 ==

===quote Suprised reply, post #555===
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!
==endquote Suprised==

==quote Atyy==
So we don't obviously need Calabi-Yau compactifications?
==endquote==

==Suprised reply to Atyy, post #556==
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.
==endquote==

 

[marcus]

This discussion is plowing deep and turning up the soil in a potentially fertile way. I reflect on on the title of the thread: "Why I am REALLY disappointed about string theory."

What has just now come up, interestingly, are not faults/limitations of theory (as I see it) but deficiencies of "program management". As I hear it, the leadership (funding committees, conference organizers) may have allowed too many "wrong turns"---so that creative talent was wasted on "blind alleys".

So a kind of meta-question would be does Tom's question matter: "Does it matter why experts are disappointed about the string program?"

Or if "disappointed" is too specific, be more general and say experts show a loss of interest, loss of energy, tendency to go off into borderline areas or spend more time in other fields, loss of focus on the hard core problems---some or all these things.

If loss of focus by the best people matters to you, and if it is real, then that looks like a program management problem. Is the string leadership listening enough to what David Gross says, or for that matter, what some people in this thread are saying? Just a thought.

 

[tom.stoer]

Marcus, thanks for the summary.

... not faults/limitations of theory ... but deficiencies of "program management". As I hear it, the leadership ... may have allowed too many "wrong turns"

Hindsight is always wiser; I was listening to a talk of a great QCD guy 20 years ago. His reply to my question how to find the best way to proceed was "how shall I do the calculation if I don't know the result?" Unfortunately this approach is not available in string theory :-(

Is the string leadership listening enough to what David Gross says, or for that matter, what some people in this thread are saying? Just a thought.

They should definately listen to Gross. The problem may simply be to identify a blind spot. In order to achieve that new questions and perspectives are required.

String theory is (in my opinion) in a situation like the strong interaction with all its hadron multiplets but w/o the fundamental representation = w/o quarks. Nice relationships, but no fundamental building block.

My guess is that strings, branes, dimensions and spacetime are only "effective" descriptions valid in certain regimes.

 

[Haelfix]

My guess is that strings, branes, dimensions and spacetime are only "effective" descriptions valid in certain regimes.

That is definitely the state of the art right now. The very real possibility (which I believe Surprised has hinted at) is that this might *always* be the case. It might be that's simply how nature has made her mathematics! Actually, it might be the case for low energy QCD as well. There might simply not be a simple analytic result that humans can package up in a simple way and pretend like it covers the entire energy range perfectly.

Certainly, most of the discoveries about dualities as well as insight into the nonperturbative physics in the last 15 years has followed this road.

Then again, there are so many very intricate mathematical relations and surprises going on within String theory, that I think the original belief that there is some as yet unknown 'super structure' that controls it all is not entirely without merit either.

 

[tom.stoer]

Now that we have consensus (OK, not really, Suprised will not agree) the interesting question is how to identify the underlying theory from which all these effective string models do emerge.

 

[atyy]

Now that we have consensus (OK, not really, Suprised will not agree) the interesting question is how to identify the underlying theory from which all these effective string models do emerge.

As a layman, the main line so far seems to have been that AdS/CFT is the sector in which this underlying theory exists, so let's study it better. The main results in recent years seem to have been about integrability and the ABJM case. In here, there is also the hope that twistors may be a reformulation of the gauge theory which will generalize - Arkani-Hamed even talks about emergent unitarity.

The other line, which is a minority, but very pretty, is the West/Damour, Henneaux, Kleinschmidt, Nicolai work on E10,E11.

I remember Mitchell Porter some time ago pointed to http://arxiv.org/abs/1008.1763 as yet another line trying to formulate the underlying theory.

Naturally, I don't know the relationship between these, or if there are in fact other more important approaches, would be interested to hear from the pros.

 

[Physics Monkey]

It seems to me that holographic duality suggests that there is no simple metatheory. Of course, many of those terms are undefined so who knows if it means anything. I don't usually think of there being some kind of metaframework for gauge theory beyond the basic structures inherent in any quantum field theory, but the existence of a string metatheory along with holographic duality would seem to imply that there is such a metaframework for gauge theory. That would be cool but also surprising in my opinion.

 

[atyy]

But could one hope for non-perturbative definitions of other sectors of the theory in the same spirit?

 

[Calrid]

Now that we have consensus (OK, not really, Suprised will not agree) the interesting question is how to identify the underlying theory from which all these effective string models do emerge.

How about trying an experiment?

Ok just kidding.

That is probably the most salient reason to be disappointed though. No evidence. Disagreements about meta questions are after all just philosophical objections atm.

Nice try but no cigar is the best thing we can say atm.

Peturbative or non peturbative, back ground dependant or not, one thing science is dependent on is discernible reality.

 

[Fra]

If we take a theory to - rather than be some objective description of outcomes of all possible measurements - be one observers inferred expectations of possible measurements it can do - than it seems plausible that two interacting observers is the same thing as two interacting theories, and in addition to that that there is no objective meta theory of how the theories interact. All there can be, is a holographic connection between theories. And that the theories that we do see in nature are somehow the result of some evolutionary selection, just like one can imagine all kinds of crazy by physicall consistent orgnisms on earth, yet the organisms we do see are many but constrained.

There can't be an *inferrable* fixed super meta space of theories. If it exists, it's only in the sense of structural realism.

So my projection of string theory, I think surprised hunch that there may not exists unique timeless eternal mother theory makes perfect sense.

But that doesn't mean it can't exists an evolving meta theory that solves our problems. This evolving meta theory then IS the same thing as what we usually call effectiv theories. I mean it could be that all there is are effective theories. But what is wrongwith that? I see nothing wrong with that. On the contrary; the search beyond effective teories is the search for realism! I was hoping that after a couple of scientific revolusions we was done with that ;) But I was wrong.

Seens as inference, this is just the same thing as acknowledging that there is no ultimate eternal truth. Ie. from the point of view of LEARNING, its' wrong to FOCUS on some ultimate truth. Doing this may in fact inhibit progress. The focus should I think be on learning, without bias of some ultimate truth.

It's the description of this process, I seek. This is exactly what interacting theories is about. So I definitely defend som of these weird things of ST, MY question is merely where the methodology of string research is optimal. Ie. is future string theory the ultimate theory of theory, or do we need to rethink the entire business from scratch?

If I understand this summary right...

Loosely speaking? Many people here except surprised, at least hopes that there will be found some unique mother theory (in order to ST ot make sense)? Is that fair?

/Fredrik

 

[suprised]

Now that we have consensus (OK, not really, Suprised will not agree) the interesting question is how to identify the underlying theory from which all these effective string models do emerge.

Well I am playing advocatus diaboli here, in raising awareness that certain views that are taken for granted by most, may potentially be wrong or at least based on misleading preconceptions.

I had expressed my personal views on "the underlying theory" already here:

https://www.physicsforums.com/showpost.php?p=2867470&postcount=251

https://www.physicsforums.com/showpost.php?p=2386391&postcount=9

 

[tom.stoer]

Well I am playing advocatus diaboli here, in raising awareness that certain views that are taken for granted by most, may potentially be wrong or at least based on misleading preconceptions.

I fully understand.

My question is this: dropping uniqueness as guiding principle, do you have a something new?

 

[Calrid]

I fully understand.

My question is this: dropping uniqueness as guiding principle, do you have a something new?

Wouldn't you have to establish uniqueness as being more coherent as an axiom than not being unique first at least inductively. Philosophically it would be difficult to do I think. I don't understand the meat and potatoes of the math, but that at least is logically sound. Something new or something better in terms of an overarching meta theory. I think differences that converge are ok, but differences that don't are forbidden. So with appropriate terms you could say that the same way of describing the same thing is better than something different, but I'm not sure how you would justify that beyond an axiom without something else to weight the consequences.

Sometimes agreeing is probably not the best way to explore things perhaps is putting it too simply.

Perhaps I am misreading your point?

 

[tom.stoer]

I don't really understand what you are saying.

My idea is rather simple: up to know physics collected experimental phenomena and theoretical descriptions and tried to "unify" them via a few axioms, principles, formulas etc. QED is based on a single Lagrangian and a common understanding how to quantize it and how to extract physics. So in some way we agree on a "unique fundamental formulation" of QED. It's not one single formula, but a few formulas plus a few principes how to use them. The same applies to QCD, etc.

All what I am saying is that this was always one guiding principle in physics. If one drops this guiding principle (there is no unique formulation, there are no fundamental degrees of freedom, ... could be 5-branes, could be E8 heterotic strings, ...) there should be some replacement, a new guideline for a research program.

My question to suprised is whether he has something to offer.

 

[suprised]

My question is this: dropping uniqueness as guiding principle, do you have a something new?

Well that was a loaded remark... let's not open another Pandora's box. Just a brief comment. Think about a conformal field theory. One and the same CFT can arise in the IR limit of many different microscopic theories; a CFT can be viewed in this sense as a universality class of theories, with the defining property that they lead to the same IR physics.

In perturbative string theory, CFTs appear as part of the world-sheet theory, and each choice corresponds to a classical background, and defines some on-shell physics (because the equations of motion are equivalent to requiring conformal invariance). One may speculate that going away from conformality is like going off-shell, and a priori it is unclear whether doing this is unique or not. In fact, it is known that a given on-shell theory may have different off-shell completions. So it may be that there is a bunch of "different" underlying theories that lead all lead to the same on-shell physics.

Essentially, this boils down to semantics and what one means by "unique" underlying theory. Eg., is lattice QCD a "different" theory as compared to the usual perturbative lagrangian formulation of QCD? No, because when performing the proper limits it lies in the same universality class. A similar phenomenon could happen eg for LQG and strings, etc.

 

[atyy]

Well that was a loaded remark... let's not open another Pandora's box. Just a brief comment. Think about a conformal field theory. One and the same CFT can arise in the IR limit of many different microscopic theories; a CFT can be viewed in this sense as a universality class of theories, with the defining property that they lead to the same IR physics.

In perturbative string theory, CFTs appear as part of the world-sheet theory, and each choice corresponds to a classical background, and defines some on-shell physics (because the equations of motion are equivalent to requiring conformal invariance). One may speculate that going away from conformality is like going off-shell, and a priori it is unclear whether doing this is unique or not. In fact, it is known that a given on-shell theory may have different off-shell completions. So it may be that there is a bunch of "different" underlying theories that lead all lead to the same on-shell physics.

That would be really nice. Is there any construction that does give the off shell theory from a QFT, or something in that direction? (I assume this is in a completely different direction from AdS/CFT?)

 

[marcus]

... "different" underlying theories that lead all lead to the same on-shell physics.

Essentially, this boils down to semantics and what one means by "unique" underlying theory. Eg., is lattice QCD a "different" theory as compared to the usual perturbative lagrangian formulation of QCD? No, because when performing the proper limits it lies in the same universality class. A similar phenomenon could happen eg for LQG and strings, etc.

The new formulation of LQG has analogies with both lattice QCD and diagram QED. The way the combinatorial structures (spin networks, spinfoams) are defined makes them analogous to both generalized lattice and Feynman diagram. 1102.3660 talks about this if I remember right.

The main difference from lattice QCD, I think, is that the lattice is irregular and has no "metric" content, no fixed edgelengths etc. The main difference from Feynman diagrams is that you have a 2-cell complex instead of a 1-cell (graph). The vertices are still places where an interaction occurs.

"...phenomenon could happen eg for LQG and strings,.." I take to suggest that some type of LQG spinfoam model could turn out to be the combinatorial cousin of some type of String model. I'm not sure what I mean by that. Perhaps there is no definite meaning at this point. Just a vague notion.

Do you watch NCG? Are you familiar with the "almost commutative space" C(M) x F where F is the finite noncommutative piece? Any ideas about this mysterious F entity?

 

[tom.stoer]

@suprised: very good point, the "off-shell d.o.f." do not matter as long as the on-shell results are correct. [but in QCD there seem to be a very good reasons to identify quarks and gluons as the fundamental d.o.f. - even if they cannot be identified as real on-shell particles]

 

[suprised]

there any construction that does give the off shell theory from a QFT, or something in that direction?...

Roughly, in QFT with perturbative lagrangian formulation this is built in. The issue arises for string theory, which is a priori formulated as an on-shell, S-matrix theory.

Constructing an off-shell theory is what string field theory aims for. One hopes that this would shed light on issues like how to "compare" different vacua, how to describe transitions between different vacua, vacuum selection, etc.

 

[suprised]

Do you watch NCG? Are you familiar with the "almost commutative space" C(M) x F where F is the finite noncommutative piece? Any ideas about this mysterious F entity?

Not really...it's still another kind of generalized geometry and to me it is unclear why NCG would be able to answer any of the open questions that we already have in other approaches.

 

[Fra]

Constructing an off-shell theory is what string field theory aims for. One hopes that this would shed light on issues like how to "compare" different vacua, how to describe transitions between different vacua, vacuum selection, etc.

This is interesting.

I know this is an open question, but if I ask for your expectation here: Do you think that the "description" which allows comparasion/(define a measure?) between diffferent vacua

1. requires an external context, that in some mathematical/realist realm allows this? If so, what happens with time, does these transition take place in some time?

2. or do you think the solution context will attach holographically to anothre vacua? Ie. that two vacuas can be compared, only with respect to a third vacua? So that rather than some external description of the landscape, you have only intrisic descirptions where the effective landscape can instead be reduced, and thus allow selection?

If 2 - is there any chance that in order to do this, the landscape will be yet bigger?

/Fredrik

 

[Calrid]

I don't really understand what you are saying.

My idea is rather simple: up to know physics collected experimental phenomena and theoretical descriptions and tried to "unify" them via a few axioms, principles, formulas etc. QED is based on a single Lagrangian and a common understanding how to quantize it and how to extract physics. So in some way we agree on a "unique fundamental formulation" of QED. It's not one single formula, but a few formulas plus a few principes how to use them. The same applies to QCD, etc.

All what I am saying is that this was always one guiding principle in physics. If one drops this guiding principle (there is no unique formulation, there are no fundamental degrees of freedom, ... could be 5-branes, could be E8 heterotic strings, ...) there should be some replacement, a new guideline for a research program.

My question to suprised is whether he has something to offer.

Yes and I was pointing out the dangers of assuming axioms without proofs. But ok.

Is it better to search for common ground or better ground is a loaded question true its also something that cannot be answered without some means to distinguish something other than maths. I would therefore say that its a moot point and that any formulation that works whether it agrees with any other or not is equal, and you don't need to agree on anything, after all hypothesis is about imagination. It's only the scientific method that distinguishes ideas from reality. Hard to say is it better to have infinite ideas all things being equal that are all different or infinite ideas that are all the same? I'd say that was a contentious question. If I had to make a judgement call I'd say meh all ideas are good congruent or not.

 

[suprised]

Fra, I guess it's better to close the Pandora's box again ;-) I can't give reasonable answers to your questions. These matters are very speculative and potentially just create more confusion than necessary.

 

[atyy]

Constructing an off-shell theory is what string field theory aims for. One hopes that this would shed light on issues like how to "compare" different vacua, how to describe transitions between different vacua, vacuum selection, etc.

Are these the same or different as trying to find non-perturbative formulations of string theory (ie. the S-matrix on a fixed background only gives perturbative string theory)?

 

[tom.stoer]

Could it be that the missing off-shell formulation was another wrong turn? (I do not know much about string field theory but it seems that it's not an active research topic).

 

[atyy]

Could it be that the missing off-shell formulation was another wrong turn? (I do not know much about string field theory but it seems that it's not an active research topic).

Taylor's http://arxiv.org/abs/hep-th/0605202 seems to indicate not so much a lack of interest, in fact, it was even hoped that this would provide manifest background independence - but more that they got really stuck in mathematical difficulties.

 

[negru]

Note that the work on ads4/cft3 is in large part motivated by applications of the high spin side to closed string field theory. The usual string theory with ever increasing masses could be coming from something else...where some symmetry is unbroken and all states are massless.

 

[suprised]

Could it be that the missing off-shell formulation was another wrong turn? (I do not know much about string field theory but it seems that it's not an active research topic).

This is a good question - many people believe that string field theory should be developed in order to ever get a handle at background indepence, vacuum selection, etc. but the program didn't really get far, so that's why not many work on this today. Perhaps it's a red herring, perhaps it is an essential missing point - who knows ;)

 

[Fra]

Taylor's http://arxiv.org/abs/hep-th/0605202 seems to indicate not so much a lack of interest, in fact, it was even hoped that this would provide manifest background independence

The paper Atyy linked to touches upong the question I asked surprised about.

2. or do you think the solution context will attach holographically to anothre vacua? Ie. that two vacuas can be compared, only with respect to a third vacua?

"Any quantum theory of gravity which attempts to deal with the landscape
of string vacua by constructing different vacua as solutions of a
single theory in terms of a single set of degrees of freedom will face
this field-redefinition problem in the worst possible way. Generally, the
degrees of freedom of one vacuum (or metastable vacuum) will be defined
in terms of the degrees of freedom natural to another vacuum
(or metastable vacuum) through an extremely complicated, generically
quantum, field redefinition of this type. This presents a huge obstacle
to achieving a full understanding of quantum cosmology. This obstacle
is very concrete in the case of string field theory, where it will make it
difficult to describe the landscape of string vacua in the language of a
common theory. It is also, however a major obstacle for any other attempt
to construct a background-independent formulation of quantum
gravity (such as loop quantum gravity or other approaches reviewed in
this book). Only the future will tell what the best means of grappling
with this problem may be, or if in fact this is the right problem to pose.
Perhaps there is some radical insight not yet articulated which will make
it clear that we are asking the wrong questions, or posing these questions
in the wrong way."
-- http://arxiv.org/abs/hep-th/0605202

I think a clue here is to see that the core of this problem is not specific to a particular program. It just tends to "show up" in different ways. And maybe it alone suggest that we need a new way of thinking of what a theory is. Should we think of theories as descriptions of reality, that are either wrong or corroborated, or should we think of theories as interaction tools?

ie

but more that they got really stuck in mathematical difficulties.

isn't the situation here suggesting something much worse than just mathematical difficulties? If it is that we simply are conceptually confused about certain things here, it's not a mathematical problem. One problem seems to shave out and separate conceptuallt unclear questions from technical problems of conceptually clear questions.

/Fredrik

 

[atyy]

The paper Atyy linked to touches upong the question I asked surprised about.

"Any quantum theory of gravity which attempts to deal with the landscape
of string vacua by constructing different vacua as solutions of a
single theory in terms of a single set of degrees of freedom will face
this field-redefinition problem in the worst possible way. Generally, the
degrees of freedom of one vacuum (or metastable vacuum) will be defined
in terms of the degrees of freedom natural to another vacuum
(or metastable vacuum) through an extremely complicated, generically
quantum, field redefinition of this type. This presents a huge obstacle
to achieving a full understanding of quantum cosmology. This obstacle
is very concrete in the case of string field theory, where it will make it
difficult to describe the landscape of string vacua in the language of a
common theory. It is also, however a major obstacle for any other attempt
to construct a background-independent formulation of quantum
gravity (such as loop quantum gravity or other approaches reviewed in
this book). Only the future will tell what the best means of grappling
with this problem may be, or if in fact this is the right problem to pose.
Perhaps there is some radical insight not yet articulated which will make
it clear that we are asking the wrong questions, or posing these questions
in the wrong way."
-- http://arxiv.org/abs/hep-th/0605202

I think a clue here is to see that the core of this problem is not specific to a particular program. It just tends to "show up" in different ways. And maybe it alone suggest that we need a new way of thinking of what a theory is. Should we think of theories as descriptions of reality, that are either wrong or corroborated, or should we think of theories as interaction tools?

ie

isn't the situation here suggesting something much worse than just mathematical difficulties? If it is that we simply are conceptually confused about certain things here, it's not a mathematical problem. One problem seems to shave out and separate conceptuallt unclear questions from technical problems of conceptually clear questions.

/Fredrik

Yes, that's what Taylor himself says. OTOH, aren't the important mathematical difficulties always conceptual ones (unless you are Euler or Ramanujan)?

 

[Fra]

OTOH, aren't the important mathematical difficulties always conceptual ones (unless you are Euler or Ramanujan)?

I'm not Euler but I'm not sure I would agree. Certainly the development of new mathematics, is a creative process, so in that sense yes they are related.

But sometimes I have a distinct feeling that people does not SEE the conceptual issues (as they are often dismissed as philosophy) and instead get occupied with technical excercises. But I don't think it's due to ignorance, it seems to be more pragmatic reasons. Some questions are simply too diffucult, and therefore it's easier to try to find an easier question.

This is what I mean with making the difference.

Rovelli ones said in a talk or some book that, even if diversions are enligtening, one should never loose focus of the real problem. (context was: don't focus on 2+1 quantum gravity just because it's easier than 3+1)

/Fredrik

 

[tom.stoer]

There is an important distinction between technical and conceptual issues.

Let's make some examples:

We can ask "why is space four-dimensional". Then it's of course conceptual question whether this should be an input to our theory or whether it can somehow be derived. One has to find a framework whioch allows one to ask these questions, based on which we are able to formulate a theory which is dimension-agnostic at all, or which allows for a different number of dimensions. The question why 6 out of 10 dimensions shall be compactified in certain string models is not conceptual. It's over, the interesting things already happened when chosing a certain background. It's no longer possible to ask the interesting questions. One can go through all CY compactifications and study their properties but one will never find out the answer to the original question.

In that sense string theory seems to ask too many technical questions instead of conceptual ones. Finding new vacua in the landscape may be interesting, but it does not help to understand deeper problems. Looking at the shape of the Earth and some atlases does not explain why the Earth is nearly spherical.

In that sense most string reserach programs do not address the fundamental issues. CY compactification, D-branes, nearly MSSM models, ... are so to speak phenomenological models. How close can one get to the real world? Arbitrary clsose I would say. What would happen if at some day the the standard model is reproduced by such a string vacuum exactly? What would we learn? Nearly nothing.

My feeling is that there is some kind of huge duality, but string theory is exactly the wrong point to start with. Whenever one wants to make any calculation one immediately leaves string theory, derives some low-energy limit and studies ordinary SUSY or SUGRA gauge theory. That's not what I am expecting from a fundamenal theory. In QCD there are w/o doubt problems that cannot be derived from QCD by first principles. I think low-energy pion-nucleon scattering is still best understood in chiral-effective theories, not in QCD. But there are many topics which can be addressed in QCD (DIS and scaling violations, lattice calculations, QGP). In string theory (this is my perception) one immediately leaves string theory and steps to some effective theory which allows in a certain limit to ask (and answer) rather specific questions. But if string theory is the fundamental theory, then we should ask (and answer) these questions in string theory, otherwise something is fundamentally wrong.

That's the reason why I guess that string theory is exactly the wrong place to start. My expectation is that string theory is correct in some sense, but that it has to be replaced by a fundamental theory from which strings, branes, backgrounds and compactifications, perhaps even dimensions can emerge.

 

[mitchell porter]

In that sense most string reserach programs do not address the fundamental issues. CY compactification, D-branes, nearly MSSM models, ... are so to speak phenomenological models. How close can one get to the real world? Arbitrary clsose I would say. What would happen if at some day the the standard model is reproduced by such a string vacuum exactly? What would we learn? Nearly nothing.

Just to be specific, let me refer to http://arxiv.org/abs/1103.4800" , which is presented as a candidate for the real world. What would it mean if that became our standard model? It would have some "particle physics" implications - in this case, the existence of a fourth generation - and it is normal for such models to imply something extra (e.g. supersymmetry). Also, quantities like the particle masses would now be understood as expectation values of geometric moduli; in this case, the resting point of a stack of branes in a six-dimensional hypertorus. We would have passed from thinking abstractly about the possibility of braneworlds, to dealing with the fact that a particular braneworld model exactly matched the data.

That's all quite a lot. It's not the same as an explanation for why that configuration of braneworlds, or what the fundamental physical picture is, but it would be an extremely revolutionary development.

 

[tom.stoer]

Good point. The question is why do we need string theory to address these questions and to study this specific model? That's what I meant with "Whenever one wants to make any calculation one immediately leaves string theory, derives some low-energy limit and studies ordinary SUSY or SUGRA gauge theory. That's not what I am expecting from a fundamental theory."

In which sense is string theory required to study this specific model? Would we learn anything beyond this specific SUSY gauge theory in the sense that it tells us something regarding string theory itself?

The benefit I see is that string theory constrains and guides model building; that's a great achievement. But once one studies a single model I have the feeling that one does not learn anything regarding string theory anymore - just something reagarding a specific model (I agree that this model seems to be interesting and that one might expect some experimental hints in similar directions).

 

[suprised]

Just to be specific, let me refer to http://arxiv.org/abs/1103.4800" , which is presented as a candidate for the real world. What would it mean if that became our standard model? It would have some "particle physics" implications - in this case, the existence of a fourth generation - and it is normal for such models to imply something extra (e.g. supersymmetry). Also, quantities like the particle masses would now be understood as expectation values of geometric moduli; in this case, the resting point of a stack of branes in a six-dimensional hypertorus. We would have passed from thinking abstractly about the possibility of braneworlds, to dealing with the fact that a particular braneworld model exactly matched the data.

That's all quite a lot. It's not the same as an explanation for why that configuration of braneworlds, or what the fundamental physical picture is, but it would be an extremely revolutionary development.

The problem with that is that there is most likely a huge variety of very similar models and there is absolutely no reason why the model one picks would describe nature exactly. Most likely one would need to readjust the model all the time, while experimental data trickle in. If this would converge in a reasonable amount time, well then OK, but I don't think this to be likely.

I guess the last 20 years have shown that there is little hope to get substantially beyond toy model status. And what's wrong about that? Many other things in nature cannot be explained/computed to high detail. And it is highly non-trivial that many qualitative features of the standard model work out well in string theory, and even important conceptual points like "explaining" the smallness of the cosmological constant in terms of a landscape can be captured in terms of phenomenogical toy models. My attitude would be not to try to ask too much.

 

[tom.stoer]

My attitude would be not to try to ask too much.

Surrender?

 

[suprised]

There is an important distinction between technical and conceptual issues.

True. But one shouldn't forget that things must work out technically, at least to some convincing degree, otherwise conceptual issues are pure speculation/philosophy. What fascinates many string physicists is that the theory works technically so well. I guess these computational results are much more non-trivial than non-experts can appreciate.

We can ask "why is space four-dimensional". Then it's of course conceptual question whether this should be an input to our theory or whether it can somehow be derived. One has to find a framework whioch allows one to ask these questions, based on which we are able to formulate a theory which is dimension-agnostic at all, or which allows for a different number of dimensions. The question why 6 out of 10 dimensions shall be compactified in certain string models is not conceptual. It's over, the interesting things already happened when chosing a certain background. It's no longer possible to ask the interesting questions. One can go through all CY compactifications and study their properties but one will never find out the answer to the original question.

In that sense string theory seems to ask too many technical questions instead of conceptual ones. Finding new vacua in the landscape may be interesting, but it does not help to understand deeper problems. Looking at the shape of the Earth and some atlases does not explain why the Earth is nearly spherical.

In that sense most string reserach programs do not address the fundamental issues. CY compactification, D-branes, nearly MSSM models, ... are so to speak phenomenological models. How close can one get to the real world? Arbitrary clsose I would say.

Fully agreed.

What would happen if at some day the the standard model is reproduced by such a string vacuum exactly? What would we learn? Nearly nothing.

Well if the string model would be fully correct and if one could do computations with arbitrary precision, one could generate infinitely many predictions.

My feeling is that there is some kind of huge duality, but string theory is exactly the wrong point to start with. Whenever one wants to make any calculation one immediately leaves string theory, derives some low-energy limit and studies ordinary SUSY or SUGRA gauge theory.

That's not quite correct, although many poeple do it that way, and that's what I criticised above. This concerns phenomenological investigations. But many investigations deal precisely with conceptual stringy features, see for example microstates in black holes, high energy scattering, etc. The AdS/CFT duality is another example of conceptional works that did not come out of a phenomenological direction. There IS a considerable effort into formal/conceptional directions, perhaps this is generally not so visible because not so many people do it and because these things may be hard to understand by non-experts.

That's the reason why I guess that string theory is exactly the wrong place to start. My expectation is that string theory is correct in some sense, but that it has to be replaced by a fundamental theory from which strings, branes, backgrounds and compactifications, perhaps even dimensions can emerge.

I would say: string theory, as formulated as an on-shell theory, is useful to describe certain features (like particle spectrum, black holes microstates, etc), but this formulation has its limitations when it comes to dynamical issues like vacuum selection.

Surrender?

Why surrender? This is research in progress, and one shouldn't try to make too large steps at once, nor generate too high expections for quick success.

 

[tom.stoer]

That's not quite correct, although many poeple do it that way, and that's what I criticised above. ... There IS a considerable effort into formal/conceptional directions, perhaps this is generally not so visible because ...

I would say: string theory, as formulated as an on-shell theory, is useful to describe certain features (like particle spectrum, black holes microstates, etc), but this formulation has its limitations when it comes to dynamical issues like vacuum selection.

OK, thanks for the explanation. I think I have to study the relevant papers more carefully. But I think we should really add background-dependence and focus on on-shell formulation to your list ...

 

[smoit]

There is an important distinction between technical and conceptual issues.

Let's make some examples:

We can ask "why is space four-dimensional". Then it's of course conceptual question whether this should be an input to our theory or whether it can somehow be derived. One has to find a framework whioch allows one to ask these questions, based on which we are able to formulate a theory which is dimension-agnostic at all, or which allows for a different number of dimensions. The question why 6 out of 10 dimensions shall be compactified in certain string models is not conceptual. It's over, the interesting things already happened when chosing a certain background. It's no longer possible to ask the interesting questions. One can go through all CY compactifications and study their properties but one will never find out the answer to the original question.

The question above might as well be technical in its nature. Let's say we want to obtain 3+1 large space-time dimensions while having the rest of them compactified on a CY 3-fold.
Let us restrict to the cases where the large dimensions are either Minkowski or nearly de Sitter to avoid the cosmological solutions with a big crunch.

Apriory, even if we assume such a compactification, we don't know if the compactified dimensions can actually remain compact until we find a reliable mechanism to stabilize all the moduli that parameterize the deformations of the internal metric. A canonical example is the Type IIB flux compactifications, where fluxes only stabilize the complex structure moduli and the axio-dilaton while the Kahler moduli remain unfixed. Stabilizing the remaining moduli is paramount for keeping the internal manifold compact. However, this task is highly non-trivial. In order to fix the Kahler moduli one must satisfy certain topological conditions that determine the number of fermionic zero modes in the corresponding non-perturbative contributions to the superpotential, which is possible in principle but extremely hard to achieve in practice, especially when charged chiral matter is present at various intersections. In addition, there is something called the overshoot problem, which in the case of multiple Kahler moduli may become a very severe problem. So, the bottom line is that in the vast majority of cases one cannot stabilize all the moduli by currently known mechanisms because one cannot generate the potential due to the topological constraints.

So, the next question would be, is it possible to stabilize all the moduli assuming a compactification down to 2+1 or 1+1 or even 0+1 dimensions?

This is not a conceptual but rather a technical question, which would require some new ideas. I personally don't know if it would be possible to have a stable compactification of, say, M-theory on a CY 5-fold or some toroidal orbifold so that all 10 spatial dimensions are compact but the vacuum energy is nearly zero. My guess is that it would be a really tough problem and it is quite possible that there are just not enough ingredients to generate a potential to stabilize all the moduli, in which case, some internal cycles will never be stabilized and will get as large as the corresponding dynamics allows them to get.

 

[smoit]

The problem with that is that there is most likely a huge variety of very similar models and there is absolutely no reason why the model one picks would describe nature exactly. Most likely one would need to readjust the model all the time, while experimental data trickle in. If this would converge in a reasonable amount time, well then OK, but I don't think this to be likely.

I guess the last 20 years have shown that there is little hope to get substantially beyond toy model status. And what's wrong about that? Many other things in nature cannot be explained/computed to high detail. And it is highly non-trivial that many qualitative features of the standard model work out well in string theory, and even important conceptual points like "explaining" the smallness of the cosmological constant in terms of a landscape can be captured in terms of phenomenogical toy models. My attitude would be not to try to ask too much.

To me, the number one problem with this Type IIA model is that the moduli are assumed to be stabilized somehow, and they go from there and compute various parameters. But the truth is that it's not at all clear if it's even possible to stabilize all the moduli in such toroidal Type IIA compactifications. IMHO, this and similar models are dead from the start until one demonstrates explicitly how all the moduli can be stabilized. Just to remind everyone, it has been shown that it is possible to fix all the moduli in massive Type IIA supergravity, which is NOT what one really wants, and the vacua one obtains are AdS with or without SUSY. The only examples of dS vacua in Type IIA that I'm aware of are the ones constructed by Eva Silverstein for compactifications on nil manifolds.