Is String Theory Still a Viable Path to a Theory of Everything?

[tom.stoer]

I am not talking about the solutions of gauge theories, but only about the gauge theories themselves. In ST you must (to a certain extend) solve the theory (construct a vacuum) in order to learn about the particle content. In gauge theory this much simpler, the particle content follows from group representation theory.

The difference is that in ST you are "constructing theories" whereas in gauge theory you already have them at hand. So there should be some benefit to let ST produce all these gauge theories instead of simply taking them, especially because the one you are interested in is already well understood. So all other theories (except for the SM) are just ballast and you want them to go away - but you don't know how this can be achieved.

OK, I see some benefits
- as I said, ST somehow constrains the theory space
- it adds quantum gravity
- it may provide a further selection principle which is unikely in gauge theories (anomalous is not restrictive enough)

Is there something like a new principle at the horizon? I do not count holography because it sems to be too weak and not very specific to string theory.

 

[BenTheMan]

in a theory which produces zillions of low-energy models, there should be some additional principle which singles out the SM (or at least a class of models containing the SM).

How is this any different from the case in quantum field theory? Does quantum field theory predict anything quantitative?

 

[Fra]

In the end it boils down to solve the landscape problem. There a couple of possibilities:
- the probability of all (fairly different) vacua is more or less equal
- the probability of some vacua is rather high
- we sit in a typical vacuum
- there is a (yet unkonw) selection principle

I'm far from convinced that one of the "set of possible models" implied from ST, can give a timeless description of reality, this is why I think we need to understand the nature of physical law - this is yet a deep question that ST at least originally didn't pose, wether the landscape problem forces some ST theorist to reassess might possible though.

What if there is no unique objective choice of vacuum or manifold even that makes sense in all situations? what would that tell us? and instead the choice of vacuum corresponds to the choice of observer? And that the choice of observer ultimately is tied to the population of observers in this world, and that an evolutionary picture is the only way to address that, that's something that would make sense to me, but then we need to still ask different questions.

Just because we understand darwins theory of evolution, doesn't mean it's possible to from a hypothetical early Earth even quantify the "probability" that the scottish would play bag-pipe. But then, that maybe isn't even a proper question since no-one at that time would be able to formulate that question. ie that "possibility" was't even on the map.

I personally think one reason for the landscape problem is the combination of structural realism with the idea a generic unification principle that can allow everything, because:

When we require an "observer independent theory", at the same time as considering the "most general" observer, it's pretty clear what happens - The complexity blows up and becomes overwhealming and useless, it's no surprise.

What if one observer instead would ask how different "observer dependent" theories interact and evolve, along with the observers? this would be a more physical view of theories, where there is not only a mathematical description of physics, but also a physics to the mathematics in the sense that complexity is constrained.

As I see it, ST originally at least never asked these things - but the landscape problem, almost "forces" these questions to be asked as they become unavoidable.

/Fredrik

 

[tom.stoer]

How is this any different from the case in quantum field theory? Does quantum field theory predict anything quantitative?

Of course it does.

First of all you have to specify the process and e.g. an energy scale in order to calculate something quantitatively.

There are perturbative regimes and non-perturbative regimes. Perturbative regimes are typically appropriate for scattering, but even in scattering non-perturbative effects can become visible. The failure of perturbation theory can be seen within perturbation theory to some extend; see e.g. the QCD scale parameter and the running coupling.

Lattice gauge theory is a way to study the non-perturbative regime of QCD with great accuracy; I think they can calculate hadron masses, some form factors etc. within 5% accuracy = 5% deviations from experimental values.

So the success of quantum field theory is that it makes quantitative predictions with great accuracy.

 

[Fra]

How is this any different from the case in quantum field theory? Does quantum field theory predict anything quantitative?

Given Tom's response I think Ben means that QFT itself is just the framework for the SM. This framwork itself does not explain the "parameters" of the SM, couplings, masses etc. All that is merely infered from experiment, with the help of the framework.

So I guess at first sight one may have the same view to ST - that the ST framework can not replace experimental feedback and that the paramters of ST (including the choice of vacumm) is an issue for experiment.

So to ask "why this vacuum" is to task why the paramters of SM are the way they are. Which is better or worse?

That may seem a reasonable attitude but IMHO it misses what I think is that a theory is really like a tool for interaction. The context where the theory lives and is defined (which is an observer in my view) uses the theory to act towards it's environment. So from a science perspective a theory not only condeses our knowledge, it also helps us pose the next question, or the next experiments to invest it. Here issues like possible gain but also possible risk needs to be addressed. It's like in biological evolution, there is a balance between diversity (potential to find more fit combinations) and the risk of exctinction if the variation is too uncontrolled.

Therefor I question the rationality behind claiming the landscape of vacuua, without selection principle. I think the fact that this has occurred indicates something strange in the learning process (á la ST).

So the major difference between ST and SM in this sene, is that althouhg neither in a deeper sense explains the origin of parameters the SM paramamters are already known, thus at this point constitute part of our "prior-background" in the information sense. In a rational learning process, one would always question, and improve the current knowledge, but it can only be done relative to the current state. There is no external judge.

So IMO the reason why ST is not preferred over SM and QFT is then that it has spent disproportionate investments in inflating the map to the extent that there is no way to nagivate. I find this from a "learning model perspective" to be irrational. But that's my personal view.

IMHO, these are the questions that I think we need to ask. But neither SM nor ST addresses this, but neither does LQG.

/Fredrik

 

[tom.stoer]

Given Tom's response I think Ben means that QFT itself is just the framework for the SM. This framwork itself does not explain the "parameters" of the SM, couplings, masses etc. All that is merely infered from experiment, with the help of the framework.

So I guess at first sight one may have the same view to ST - that the ST framework can not replace experimental feedback and that the paramters of ST (including the choice of vacumm) is an issue for experiment.

But then we must ask if it makes sense to use ST in order to parameterize a mass or a coupling constant in terms of a vacuum / moduli space instead of using a number; what's the benefit?

 

[BenTheMan]

Of course it does.

I think you're a bit confused about either my question, or the predictive power of the quantum field theory.

Given the edifice of quantum field theory, can you predict a unique set of consequences in a low energy theory? Can you predict that there should be three generations? Are there any consistency conditions which uniquely determine low energy physics?

So, for example:

Lattice gauge theory is a way to study the non-perturbative regime of QCD with great accuracy

Can you explain to me how this calculation works? Specifically, how can you derive that there are quarks and hadrons or something called QCD?

 

[BenTheMan]

But then we must ask if it makes sense to use ST in order to parameterize a mass or a coupling constant in terms of a vacuum / moduli space instead of using a number; what's the benefit?

Much can be gained from the analogy with quantum field theory, which is why I pointed this out in the first place :)

String theory makes generic predictions about physics, in the same way that quantum field theory makes generic predictions about physics. Most people who work in the field (myself included) view string theory as a framework for generating interesting quantum field theories. All quantum field theories which can possibly be built are not derivable from string theory---this is what's called the swampland, and Washington Taylor at MIT is doing some interesting work in that regard.

So, for example, quantum field theory will never tell you that you have electrons, but if you measure electrons in a lab, quantum field theory predicts that you should also measure positrons. In this sense, quantum field theory itself is not very predictive. All predictions come from first specifying a model, THEN using the tools to extrapolate predictions. In other words, we start with an observation, we try to construct a model which matches what we've observed, then we try to make new predictions based on the model. This is how the Standard Model was born, so why should we think that quantum gravity would follow different rules?

 

[Fra]

But then we must ask if it makes sense to use ST in order to parameterize a mass or a coupling constant in terms of a vacuum / moduli space instead of using a number; what's the benefit?

Yes. Unless supplied with a selection principle, from the inference perspective I find it detrimental.

I could personally defend one general trait from ST, and it's the idea to find a unifying microstructure or system therof from a general action follows as per some procedure.

But this only makes sense (ie. increases the fitness of our understanding) if supplied with a measure of preference where to place your bets.

The problem IMO, is the starting point for this construction in ST is a continuous string, that is pictures to live in an external fixed space. I have no faith in that specific idea. My main objections concerns the continuum.

My one hope for ST, is reformulation of it's very basics to get rid of the contiuum string, and instead replace it with sometihng more general that has finite complexity, and does not introduce a full continuum of complexions as from an inference perspective that just doesn't make sense. If this is done, there would be no massive landscape since the state space of possible actions would be constrained by complexity. At unification scale, the number of possibilities must approach 1, the landsccape would increase as t he complexity does (as massive observer emergen) but then along with that inflation of state space is also the selection process, so the landscape should still be truncated as it evolves.

But that is very radical as opposed to ST. I just see similarities.

/Fredrik

 

[humanino]

Can you explain to me how this calculation works? Specifically, how can you derive that there are quarks and hadrons or something called QCD?

Are you asking for a proof of the mathematical consistency of quantum gauge field theories ?

From a practical point of view, the mathematically unjustified lattice calculations can not reasonably be described in a few sentences, as you know we have textbooks devoted to them. Also from a practical point of view, it is true that a few approximations in LQCD are not very well under control for certain observables. I think however you are not asking for practical matters, but for matters of principle.

I believe it is not controversial that :

• there is a large consensus that quantum gauge field theories can be made consistent mathematically
• there is a large consensus that Feynman diagrams are not the "right" way to think/compute with them (c.f. MVH amplitude in multi-gluon scattering and the offspring of Witten's 2003 twistor string paper).

So from the two above observations, we know that there is a rapidly growing field indicating that our knowledge is not ripe for a proper mathematical definition of quantum gauge field theories.

So unless I misunderstood the question, it does not appear very fair to me : what are you trying to suggest ?

 

[BenTheMan]

So unless I misunderstood the question, it does not appear very fair to me : what are you trying to suggest ?

I was just trying to make the point that QFT does not predict QCD, that's all.

 

[humanino]

I was just trying to make the point that QFT does not predict QCD, that's all.

I see that I seriously missed your point.

I'll quote Wilzeck, who asked Dyson
"What is the single most important thing you learn from quantum field theory, that you don't already know from quantum mechanics and field theory separately ?"
"Why, that all electrons are the same, of course !"
Related in "Fantastic realities", one can also read his contribution to the Centenary issue of Rev. of Mod. Phys.

 

[Fra]

All quantum field theories which can possibly be built are not derivable from string theory---this is what's called the swampland, and Washington Taylor at MIT is doing some interesting work in that regard.

I understand and appreciate this, and it's analogous to what I mean when I think of "inferrable laws". Not all laws, or information states that are "mathematically possible" are physically possible. In particular do I think it's not possible for a finite observer, to infer anything involving certain konwledge of infinitely resolved things like continuum structures.

So you say that only theories that consitructable via ST framework are physical? And in this ST framwork includes and idea based on the microstructure and action of your elementa, the string.

I would say that only instrisically inferrable theories are physical. In this is included an idea (to be worked out) about the properties of a generic inference system and how it evolves, and how it implies an "entropic action".

So I really appreciate this "dimension" of ST, I would take this serious in principle. BUT, if this is the way to see it, I think that there really is lacking some serious arguments on why we should have faith in the CHOICE OF inference system.

In my view, the string model, is a very special case and it seems like a strange starting point. I expect the argument to come from basic inference of reasoning upon incomplete information. Wthout that, we are back to the case where the only "hard arguments" solid predictions.

As I see it, the thing that ST aspires to be - a framework for "constructing" the physically possible theories (as opposed to more wildly any mathematically possible) - is an admirable ambition, but it's exactly in this ambition that I think ST is weak.

This is why I both see good traits in ST, but at the same time don't like it. I guess I wish some string theorist, could motivate ST "as the framework" it is, rather than something that gives definite predictions. I have not seen anyone doing that, and maybe it's because there is no good motivation?

/Fredrik

 

[BenTheMan]

So you say that only theories that consitructable via ST framework are physical?

I want to be very clear that this is not what I'm claiming: there is no evidence for this claim in 4 dimensions. Washington Taylor and collaborators have shown that this is a true statement in 10 dimensions (http://arxiv.org/abs/1006.1352). From the abstract:

We show that the N=1 supergravity theories in ten dimensions with gauge groups U(1)^{496} and E_8 x U(1)^{248} are not consistent quantum theories. Cancellation of anomalies cannot be made compatible with supersymmetry and abelian gauge invariance. Thus, in ten dimensions all supersymmetric theories of gravity without known inconsistencies are realized in string theory.

I hope that the importance of this result is grasped: there exist no supergravity theories in ten dimensions which cannot be derived from string theory. All consistent N=1 SUGRA theories in 10 dimensions come from string theory.

In addition, they have evidence that this is true in six dimensions. That is, all fully consistent, N=1 (in 6d) SUGRA theories can be seen to come from a string theory. There are no statements about 4d physics, but that is the next logical step.

In my view, the string model, is a very special case and it seems like a strange starting point.

Why is starting with a string any more arbitrary than starting with a particle?

As I see it, the thing that ST aspires to be - a framework for "constructing" the physically possible theories (as opposed to more wildly any mathematically possible) - is an admirable ambition, but it's exactly in this ambition that I think ST is weak.

No. As Wati Taylor is showing, consistent quantum field theories only seem to come from string theory. This is the case in ten dimensions, and it seems to be the case in six dimensions. The 4d case, as I understand it, is much more difficult.

I guess I wish some string theorist, could motivate ST "as the framework" it is, rather than something that gives definite predictions. I have not seen anyone doing that, and maybe it's because there is no good motivation?]

I want to point out that I have been attempting to do exactly this in this thread. As you see: tom.stoer asked for a construction of the standard model coming from string theory, and I showed him one, to which he abruptly changed his criteria. Can I ask: what level of proof do you need? If you can't see for yourself that string theory gives you physically interesting quantum field theories which have a fully consistent embedding into quantum gravity, what other evidence do you want?

 

[tom.stoer]

tom.stoer asked for a construction of the standard model coming from string theory, and I showed him one, to which he abruptly changed his criteria. Can I ask: what level of proof do you need? If you can't see for yourself that string theory gives you physically interesting quantum field theories which have a fully consistent embedding into quantum gravity, what other evidence do you want?

I didn't want to change my criteria; if I did I think I should explain, so please tell me where I was inconsistent.

You mention the idea to constrain physical models based on string theory; or to put it the other way round that models not derivable from string theory are necessarily inconsistent mathematically or inacceptable physically. Of course this is a rather interesting approach. I see that this is work in progress, but I appreciate these ideas very much.

But maybe you are now the one who changes the criteria. ST started with the ambitious idea to (uniquely) derive the ToE; it changes to the landscape discussion where we do no longer have one theory of everything but "all theories of something". With this new turn it may change again allowing us to focus on a certain class of models - fine.

The problem is that one still needs a selection principle that allows one to select the SM. Let's assume that based on ST one can restrict the class of allowed models to 42. That is certainly much better than an infinity of models based on SU(N) and SO(N) groups; and it's worse than 5. So there is progress (I agree on that), but still no evidence, only a hint ...

 

[Haelfix]

"it changes to the landscape discussion where we do no longer have one theory of everything but "all theories of something"."

I used to make the following analogy, before I learned that it was incorrect:

String theory is one, unique completely specified theory. It has a large but finite number of vacua (not unlike GR)

QFT (gauge theory) is an uncountable infinity of theories, with a single vacua for each*

The trade off from a practical point of view, is similar in the sense that you need experiment to pin things down. However from a theoretical point of view, its much much more preferable to have the theory pinned down uniquely as opposed to having a unique solution.

*Then of course one learns that this is not true. Only a small minority of gauge theories have trivial vacua. In the last 15 years physicists have learned a great deal about realizations of symmetry, nonperturbative vacua and metastable Moduli and unfortunately the story is not as simple as was once thought. We know now that gauge theories can have enormous amounts of solutions, that were not necessarily apparent at first glance. Perhaps not so surprising given the preponderance of string dualities out there but still somewhat surprising.

Punchline being, gauge theory is far less constraining. As I said before, the only redeeming virtue is that there exists a naive measure of simplicity.

 

[tom.stoer]

String theory is one, unique completely specified theory. It has a large but finite number of vacua (not unlike GR)

... However from a theoretical point of view, its much much more preferable to have the theory pinned down uniquely as opposed to having a unique solution.

It is by no means clear that it is uniquely specified. And it is not clear that the number of vacua is finite.

But I agree that a unique thery is preferrable.

QFT (gauge theory) is an uncountable infinity of theories, with a single vacua for each

I agree.

The trade off from a practical point of view, is similar in the sense that you need experiment to pin things down.

But unfortunately ST seems to be not able to make use of experimental results.

 

[BenTheMan]

By standard model I mean the well-established standard model of elementary particle physics: U(1)*SU(2) electro-weak interaction plus SU(3) QCD. Of course this includes the symmetry structure, 6 flavor / 3 generation content, masses, couplings, mixing angles etc. Of course I do not expect all these constants to be derivable with arbitrary numerical accurancy, but I expect at least the overall picture to emerge from ST.

These models have the correct MSSM spectrum including forces, particle content (three generations of quarks and leptons) and interactions, heavy top quarks, and it can be shown that there are no light exotics. All couplings are calculable in principle, as the full yukawa structure is known.

But I think you understand what I mean by post-dict: in a theory which produces zillions of low-energy models, there should be some additional principle which singles out the SM (or at least a class of models containing the SM). Unfortunately up to know all possible low-energy models seem to be equally likely.

I will admit to coming into the discussion half-way through, but you didn't ask for a unique prediction, did you? Perhaps that criterion was in another post not directed at me?

Either way, you ARE correct that string theory does not imply the standard model---of course, quantum field theory does not imply the standard model either, which I've tried to point out, so I think the point is moot.

 

[MTd2]

Is there anything string theory must be necessarily, not just sufficiently, used to probe or explain a phenomena without having to wait for a Kardashev II civilization?

 

[Haelfix]

"It is by no means clear that it is uniquely specified. "

So long as you insist that the anomalies cancel, you have specified the theory exactly and uniquely, all the couplings are then fixed. You can parse some legalese language with regards to M theory and dualities (are they or are they not separate perse), but even if you take the extreme view still held by a few people, you end up with a maximum of 5 theories.

 

[Fra]

Why is starting with a string any more arbitrary than starting with a particle?

I have objections to a particle in a continuous space as well. So some of the critique, certainly applies to QFT as well. I guess I think ST is not radical enough. I appreciate the "framework" idea, I have not problem wit that, I just don't think it's the right CHOICE of framwork.

But the obvious argument is that if we for a second ignore the embedding, a "point" represents in my view a single distinguishability index, a string represents a continuum of them - it's simple more complex.

I want to point out that I have been attempting to do exactly this in this thread. As you see: tom.stoer asked for a construction of the standard model coming from string theory, and I showed him one, to which he abruptly changed his criteria. Can I ask: what level of proof do you need? If you can't see for yourself that string theory gives you physically interesting quantum field theories which have a fully consistent embedding into quantum gravity, what other evidence do you want?

I'm not asking for a formal proof of course, that would be unreasonable. I just find the non-formal arguments given very weak. But what's weak or not is certainly a biased opinion. The only reasons I insist putting forward these objections is that I am convinced (right or wrong) that there is a MORE general AND more selective framwork, where it's even possible that the "string" can be seen as a special case of a primordal observer. I know most string theorist just doesn't think like this, but still.

My projection of the landscape problem onto my view, is that choosing the background is simply related to the problem of "choosing observer". And the selection problem is related to predicting the population of observers in the actual universe.

But in this view, I just can't make sense of thining of the continuum string as the simpelst possible observer, as it's a continuum of distinguishable events. A continuum of distinguishable events isn't inferrable in my view. I think the continuum is also responsible for large part of the "redundancy" that has made he landscape so large.

My alternative is certainly not more clear at this point, but then again ST is a big program that has been around for years. I think if this is to be seen as a framework for generating physical theories then and inference perspective is reasonable.

/Fredrik

 

[tom.stoer]

"It is by no means clear that it is uniquely specified. "

So long as you insist that the anomalies cancel, you have specified the theory exactly and uniquely, all the couplings are then fixed. You can parse some legalese language with regards to M theory and dualities (are they or are they not separate perse), but even if you take the extreme view still held by a few people, you end up with a maximum of 5 theories.

Let me explain why I think that ST is not uniquely defined.

First of all there are the well-known 5 theories; their dualities are highly impressive, but afaik not always strictly prooven. Instead they partially rely on strong-weak coupling and/or large-N approximations. Therefore one does not know if these theories are dual, or if only their "asymptotically domains" are dual.

Second there is the perturbative "definition" of one theory. Perturbative treatment is not defined beyond 2 loops (afaik there are attempts to construct the superspace measure at 3 and 4 loops, but no results for higher genus are known). Then we know that perturbative treatment is not sufficient as a) it missing non-perturbative effects and b) the perturbation series itself may be ill-defined (as long as there is no measure for higher genus it does not even exist); but even if it exists one has to prove that the series is i) finite order by order and ii) convergent. Both proofs do not exist.

Third we have to look at non-perturbative approaches. Most results we know today are purely classical. Most D-brane caclulations are classical identifications of vacua w/o a full quantized theory on top of it. Full non-peturbative approaches are still missing.

Forth most calculations are low-energy effective theories (e.g. SUGRA, SUSY / gauge theories) derived from the zero-mass string modes. The higher modes are "integrated out" or just neglected. So many results from ST are not strictly ST but due to effective theories.

Fifth afaik there are still obstacles to define the theory fully background independent. That means it is not clear how the theory can "connect" different backgrounds dynamically. And there are backgrounds for which we do not know how to quantize the theory on top of it (the last thing I remember was that one has to restrict to "stationary" spacetimes with timelike Killing vector)

Last but not least afaik a strict definition of M-theory is still missing, even if there are some promising approaches like 3-algebras and matrix theory. But there is no established procedure how to solve the theory, not even in principle. It is not that we know what to do in principle but are not able to do the calculations in practice (as they are too complex, time-consuming etc.).

All this seems to be unfair as these requirements do not apply to quantum field / gauge theories. This is correct as one can always refer to a (unique) UV-completion beyond quantum field / gauge theory. But in string theory this is no longer possible; there is no theory beyond ST which could solve all these ST issues.

 

[BenTheMan]

It seems that most of your objections can be answered with "Sure, it's a hard problem, people are working on it". So, you can throw up your hands and give up, or you can actually try to calculate things.

Specifically, though, you even criticize the instances when people CAN calculate things:

Forth most calculations are low-energy effective theories (e.g. SUGRA, SUSY / gauge theories) derived from the zero-mass string modes. The higher modes are "integrated out" or just neglected. So many results from ST are not strictly ST but due to effective theories.

I can't claim any expertise with the other issues that you've brought up, but I DO know something about this.

Let me ask: why do you list this as a problem? The (Wilson) effective field theory can be defined, and the KK modes can be summed over, and integrated out (which is a strictly defined process, which you seem to neglect?---see Fermi Theory, for example). One can then calculate threshold corrections to the gauge couplings (for example). This was done in 1987 by Kaplunovsky, and since has been applied to most of the approaches where people actually get a complete EFT. In fact, constructing the EFT and calculating threshold corrections is a textbook exercize in, for example, the hetorotic orbifold compactifications.

 

[tom.stoer]

It seems that most of your objections can be answered with "Sure, it's a hard problem, people are working on it". So, you can throw up your hands and give up, or you can actually try to calculate things.

I only want to make clear that ST is not yet "defined" - whatever it means - but that this "definition" is still work in progress.

Let me ask: why do you list this as a problem? ... This was done in 1987 by Kaplunovsky, and since has been applied to most of the approaches where people actually get a complete EFT.

I listed this as a problem since I was not aware of the fact that a full Wilsonian approach has been carried through in ST and that this is standard for deriving SUGRA, gauge theories, etc. This is due to my ignorance, I apologize for it and delete it from my list.