Why I am REALLY disappointed about string theory

[mitchell porter]

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

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

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

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

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

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

 

[Physics Monkey]

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

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

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

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

 

[Physics Monkey]

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

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

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

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

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

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

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

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

 

[fzero]

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

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

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

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

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

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

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

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

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

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

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

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

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

 

[MTd2]

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

 

[Haelfix]

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

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

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

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

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

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

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

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

arXiv:0704.1814

 

[Fra]

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

Thanks Haelfix for your always excellent posts.

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

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

/Fredrik

 

[Physics Monkey]

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

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

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

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

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

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

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

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

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

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

 

[fzero]

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

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

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

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

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

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

 

[smoit]

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

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

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

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

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

 

[suprised]

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

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

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

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

 

[Physics Monkey]

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

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

 

[marcus]

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

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

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

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

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

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

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

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

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

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

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

 

[tom.stoer]

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

 

[marcus]

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

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

 

[suprised]

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

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

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

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

 

[suprised]

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

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

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

 

[fzero]

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

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

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

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

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

 

[marcus]

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

Excellent, thanks much!

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

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

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

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

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

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

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

 

[marcus]

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

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

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

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

I get the impression that these 8 ideas of what could have been a false step (or no longer useful way of thinking) offer a way that the String program can re-energize...

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

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

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

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

 

[ApplePion]

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

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

 

[Fra]

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

I like the direction you say here.

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

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

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

/Fredrik

 

[arivero]

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

- That geometric compactification of a higher dimensional theory is a good way to think about the string parameter space
- That perturbative quantum and supergravity approximations are a good way to understand string theory
.

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

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

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

 

[marcus]

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

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

 

[Calrid]

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

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

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

 

[Haelfix]

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

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

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

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

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

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

 

[Physics Monkey]

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

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

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

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

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

 

[smoit]

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

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

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

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

 

[fzero]

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

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

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

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

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

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

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

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

 

[arivero]

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

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