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Surrender?suprised said:My attitude would be not to try to ask too much.
Surrender?suprised said:My attitude would be not to try to ask too much.
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.tom.stoer said:There is an important distinction between technical and conceptual issues.
Fully agreed.tom.stoer said: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.
Well if the string model would be fully correct and if one could do computations with arbitrary precision, one could generate infinitely many predictions.tom.stoer said: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.
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.tom.stoer said: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.
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.tom.stoer said: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.
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 said:Surrender?
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 ...suprised said: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.
tom.stoer said: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.
suprised said: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 said:My concluson is still that we lack fundamental d.o.f.
Fra said:(Of course my preferred answer is that we should see theories not as descriptions but as interaction tools, thus all theories evolve, and no theory can be described from the outside, but rather you can only described it (from the outside) in the sense as from another theory. This is the inferential perspective.)
smoit said: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.
atyy said:But a way to construct a universe so that the inside people can make theories is to make the universe using some laws.
suprised said:It would be good to keep the discussion in this thread centered at string theory.
tom.stoer said:Let's compare the situation to QED.
In QED nobody ever proved that iron and copper do exist. Nevertheless for various reasons we simply believe that iron and copper exist "in QED". Their existece is taken for granted and we can calculate their properties (specific heat, conductivity, phonon spectrum, ...). We are rather successful with these calculations using effective models.
In string theory the existence of something like iron, copper, etc. has been shown to exist most likely. Starting with something like iron we can calculate certain properties (masses, coupling constants, ...) and again we are rather successful.
So the problem is not so much that we fail at the level of iron and copper, the problem is not that we cannot prove that iron and copper can exist. It seems that in that sense string theory is rather successful. Of course there are many technical details that have to be worked out, but that was the same in condensed matter physics as well.
The problem is that we seem to argue on the level of phonons, excitons etc. We are still on an effective level, we are not studying the fundamental theory. And we are not able to talk about the "environmental conditions" required for the existence of iron and copper. In QED we are (to a certain extent) able to specify the conditions required for the formation of certain substances, in nuclear physics we can even study / specify the conditions under which certain elements and isotops are formed. In string theory we can't do that.We can specify certain selection principles (topological constraints, moduly stabilization, ...) which are necessary pre-conditions, but the true dynamical mechanism behind the scenes, the "vacuum selection", "vacuum tunneling" etc. cannot be addressed.
My concluson is still that we lack fundamental d.o.f., background independence and an off-shell formalism - or perhaps something totally different.
atyy said:But wouldn't the conjecture of http://arxiv.org/abs/0906.0987 mean that there are some stable solutions in 6D too?
tom.stoer said: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 ...
tom.stoer said:Let's compare the situation to QED.
...
The problem is that we seem to argue on the level of phonons, excitons etc. We are still on an effective level, we are not studying the fundamental theory...
My concluson is still that we lack fundamental d.o.f., background independence and an off-shell formalism - or perhaps something totally different.
Physics Monkey said:I am very sympathetic to this point of view, but I also want to offer a little bit of counterpoint. ...
Knowing the fundamental theory is often not that helpful for doing physics at energy scales well below the fundamental scale.
... Of course, it would be great to have some off shell formulation or whatever. It's bound to tell us something, for example, about transitions between different vacua. But I don't expect that such a discovery would reduce string theory to technical questions or tell us very much about the particular vacua we happen to find ourselves in.
Tension - not more - not less.marcus said:There is an interesting tension or difference in viewpoint here between Tom and Brian. Tom suggests adding a couple of more weakpoints to Suprised list of string program "wrong steps". Actually these two are not "wrong steps" as much as they are "steps not taken".
Brian argues that perhaps they are not important steps to take because how would they help us "do physics"?
smoit said:Yeah, that's certainly possible because there are fewer moduli to worry about, but my point was to show that the more dimensions are compact, the more types of moduli one must stabilize and the more difficult the task of keeping the dimensions compact becomes. I was simply suggesting that there may be a bound on the number of dimensions that can remain compact but until one sits down and starts calculating this is just a speculation. The question is - suppose one starts with ALL spatial dimensions compact, what is the maximum number of dimensions that can possibly remain compact, i.e. the corresponding moduli can be dynamically fixed, while the rest of them have runaway directions? This is a technical question that one should be able to answer already, at least for the simple examples I had suggested, without any background independent formulation, etc. All these questions about vacuum selection ASSUME that one can obtain stable vacua but my point is that vacuum stability, i.e. having a robust dynamical mechanism for keeping all the internal dimensions compact, may just as well be a possible selection principle in addition to some other ones.
suprised said:The problem I never see addressed (probably because there is no good answer), is what forces the theory to compactify some dimensions at all. I can't think of any convincing reason why the theory with maximal symmetry (in 10 or 11d) would not be a sweet spot for the theory to stay there. Somehow the opposite of a sweet spot seems to be required (no obvious susy in lower dimensions, no unbroken E8's, etc). Apart from anthropic reasoning, which bypasses this point, there is AFAIK no mechanism or principle known that would drive the theory away from its comfortable sweet spot into the ugly messy non-susy real world we observe.
I actually don't think there will ever be such a principle, at least in the framework developed so far. As said before, I toy with the idea that what we have discovered in terms of the many string vacua, just parametrizes the space of consistent theories that include gravity. By itself, this construct would not exhibit any preferred choice of vacuum etc. It may be another "wrong" prejudice that because string theory ought to be "complete", it would somehow pick the right vacuum for us.
As said before, perhaps string theory should simply be viewed as a generalization of Yang-Mills theory that includes gravity. Then in a similar sense that N=4 Yang Mills theory does not "predict" the standard model gauge theory, the 10/11d theories do not predict the standard model including gravity (although the latter can be consistently embedded via deformation or compactification).
suprised said:Then in a similar sense that N=4 Yang Mills theory does not "predict" the standard model gauge theory, the 10/11d theories do not predict the standard model including gravity (although the latter can be consistently embedded via deformation or compactification).
atyy said:What exactly is anthropic reasoning? In perhaps older views, it is that the initial conditions were what they were because they were what they were. But in the context of string theory, I've heard that the initial conditions were what they were because all initial conditions did in fact happen.
suprised said:The problem I never see addressed (probably because there is no good answer), is what forces the theory to compactify some dimensions at all. ...
I actually don't think there will ever be such a principle, at least in the framework developed so far. As said before, I toy with the idea that what we have discovered in terms of the many string vacua, just parametrizes the space of consistent theories that include gravity. By itself, this construct would not exhibit any preferred choice of vacuum etc. It may be another "wrong" prejudice that because string theory ought to be "complete", it would somehow pick the right vacuum for us.
As said before, perhaps string theory should simply be viewed as a generalization of Yang-Mills theory that includes gravity. Then in a similar sense that N=4 Yang Mills theory does not "predict" the standard model gauge theory, the 10/11d theories do not predict the standard model including gravity (although the latter can be consistently embedded via deformation or compactification).
negru said:Well matrix theory showed that ultimately we'll get some sort of non-commutative geometry, so the usual smooth manifolds are clearly not enough. This geometry issue is equivalent to finding the "master string theory" if there is one, or at least better understanding what the fundamental degrees of freedom are in some of the theories.
Well, actually one can significantly enhance the gauge symmetries by compactifying to lower dimensions. In fact, when comparing compactifications of F-theory on CY 3-folds with those on CY 4-folds, one can obtain much bigger gauge groups in the 4-fold case than in the 3-fold case, which in turn are much bigger than those for the K3 case. The same is true for the Heterotic case, where one can also get many non-perturbative gauge groups in addition to the original E8XE8 in 10D.suprised said:The problem I never see addressed (probably because there is no good answer), is what forces the theory to compactify some dimensions at all. I can't think of any convincing reason why the theory with maximal symmetry (in 10 or 11d) would not be a sweet spot for the theory to stay there. Somehow the opposite of a sweet spot seems to be required (no obvious susy in lower dimensions, no unbroken E8's, etc). Apart from anthropic reasoning, which bypasses this point, there is AFAIK no mechanism or principle known that would drive the theory away from its comfortable sweet spot into the ugly messy non-susy real world we observe.
fzero said:An anthropic argument isn't really about initial conditions. One typically resorts to the anthropic principle when one is ignorant of the initial conditions or can't describe the vacuum state in terms of initial data for one reason or another.
One way to use the anthropic principle is the following. Imagine that we have a space of effective theories parameterized by some numbers [tex]p_i[/tex], which could typically involve coupling constants, but could be generalized to ranks of gauge groups, number of matter generations, etc. A theory is a point [tex]\vec{p}[/tex] in the space of these coupling constants. If there is some energy function on the space of couplings, then one could refer to the space of absolute minima as the space of vacua.
Anthropic arguments place bounds on the [tex]p_i[/tex] such that [tex]p^{(-)}_i < p_i < p^{(+)}_i[/tex]. The reasoning would generally be that if a parameter was out of the specified range, the universe could not have the features that it does. For example, in http://prl.aps.org/abstract/PRL/v59/i22/p2607_1 Weinberg established an upper bound on the value of the cosmological constant from the requirement that gravitationally bound systems like galaxies were allowed to form. This is a relatively weak bound, while stronger bounds might be established in a general theory by requiring tight fits with the fine structure constant, electron mass, etc. Some values, like number of generations, would be fixed to specific values, rather than a range.
If the vacua depend on discrete values of the parameters (as in string theory), then it makes sense to ask what number of vacua lie within the anthropic bounds [tex]\mathcal{N}[(p^{(-)}_i ,p^{(+)}_i)][/tex]. In some sense, the success of the anthropic argument is reflected by the value of [tex]\mathcal{N}[/tex]. One hopes that this number is small.
Initial conditions are only relevant if we have some way to compute the [tex]p_i[/tex] in terms of the initial values [tex]p^{(0)}_i[/tex]. In general this cannot be done for the vast majority of interesting string vacua.
atyy said:Let's see, I was thinking pretty much along the same lines except that I thought that each "initial condition" would pick out one vacuum. If that were the case, would that be a qualitatively similar understanding of what "anthropic" means? Also, is it technically not the case that specifying initial conditions picks out a vacuum (ie. is it too naive to reason by Newtonian analogy where initial conditions pick out the solution)?
suprised said:Somehow the opposite of a sweet spot seems to be required (no obvious susy in lower dimensions, no unbroken E8's, etc). Apart from anthropic reasoning, which bypasses this point, there is AFAIK no mechanism or principle known that would drive the theory away from its comfortable sweet spot into the ugly messy non-susy real world we observe.
smoit said:Well, actually one can significantly enhance the gauge symmetries by compactifying to lower dimensions.
negru said:But given some principle, or extra input, it could in principle predict the SM. And the same with string theory. I think it would be foolish to expect string theory to give all the Standard Model parameters without any extra input.
Can you say more about this?negru said: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.
mitchell porter said:Can you say more about this?