A No metastable type IIB de Sitter vacua

[Islam Hassan]

I agree, the relation between Occam and string theory is still unclear, and Occam is more useful in hindsight than foresight. All I'm saying is, there is a danger when a community builds an expertise that has as yet not proved to be a good theory, there can be the danger of square pegs in round holes. But they are the best ones to figure out which it is at this point-- if they can be objective.

Agreed, except perhaps that objectivity can sometimes be a wobbly issue...from what I gather mathematical objectivity is perhaps the major focus of ST today...with the hope that this will one day yield a testable physical one...in fine, objectivity is also defined in hindsight...IH

 

[Urs Schreiber]

Ken G, some information:

The KKLT 03-constructions that are being abandoned (for being wrong) were so complicated that Susskind 03 famously referred to them as "not at all simple. They are jury-rigged Rube Goldberg contraptions" (p. 5). Hence abandoning KKLT likely means to reduce the perceived complexity, not to increase it.

On the other hand, beware that there are general arguments in quantum gravity, independent of string theory, that global de Sitter spacetime is inconsistent, see e.g. Rajaraman 16 and references given there. If true, this means that no quantum consistent model for observed cosmology will be totally straightforward, all of them will have to realize a de Sitter cosmology as an effective phenomenon on the backdrop of non-de Sitter cosmology.

Hence if you are intent on doing fundamental physics by way of slogans, remember the Occam's slogan has an addendum: "as simple as possible, but no simpler".

 

[Ken G]

Ken G, some information:

The KKLT 03-constructions that are being abandoned (for being wrong) were so complicated that Susskind 03 famously referred to them as "not at all simple. They are jury-rigged Rube Goldberg contraptions" (p. 5). Hence abandoning KKLT likely means to reduce the perceived complexity, not to increase it.

That's well and good, and I don't doubt you are correct, but that's not the reduction in complexity I'm talking about-- I'm talking about the cosmological constant. It sounds like you are saying that the reason KKLT existed in the first place was because it looked like it supported a positive vacuum energy. You are saying that was never a good enough reason to adopt what is essentially wrong physics, but in arguing it is wrong, you are pointing to studies that conclude type IIB string theory is not terribly compatible with positive vacuum energy. So that's the irony here-- the killing blow to KKLT is that it concludes something that string theory prefers to violate, yet it is the thing that KKLT is trying to conclude that is the simplest explanation for astronomical observations. This in turn suggests that string theory may not be terribly compatible with Occam's Razor when applied astronomically.

On the other hand, beware that there are general arguments in quantum gravity, independent of string theory, that global de Sitter spacetime is inconsistent, see e.g. Rajaraman 16 and references given there. If true, this means that no quantum consistent model for observed cosmology will be totally straightforward, all of them will have to realize a de Sitter cosmology as an effective phenomenon on the backdrop of non-de Sitter cosmology.

That does sound significant, though of course it will also present the choice: accept awkward modifications to quantum gravity to get de Sitter, or just go with a very different approach to gravity that is built to play well with de Sitter from the get go. How much of current quantum gravity is regarded as successful, in the sense of producing expectations of things we actually see? Any of it?

Hence if you are intent on doing fundamental physics by way of slogans, remember the Occam's slogan has an addendum: "as simple as possible, but no simpler".

Calling Occam a "slogan" hardly rescues you from the problem here: physics must be done so as to give the simplest possible explanations to what we actually see. That isn't a slogan, it's the definition of scientific progress.

 

[Urs Schreiber]

What I meant to indicate regarding "slogans" is -- given that the field has suffered from people being prejudiced about what the theory should yield, without being careful about doing the actual math -- that it is wrong to react to this by just changing the prejudice about what ought to be the case. It's time to do careful analysis and let the prejudices rest for a while.

 

[Urs Schreiber]

Danielsson himself writes about the issue discussed here:

U. Danielsson: "Is string theory in crisis?" (July 8, 2018)

 

[Urs Schreiber]

I am not an expert on the matter of inhomogeneous cosmology, but in view of the above discussion it is interesting to check the latest developments here:

What is called inhomogeneous cosmology is the study of cosmology via cosmological solutions to Einstein's equations, whithout assuming or constraining these solutions to be spatially homogeneous (in the technical sense).

This is in contrast to the standard model of cosmology, based on FRW model-type solutions to Einstein's equations, where spacetime is assumed to be spatially homogeneous.

Of course the observable universe is clearly not exactly homogeneous, but the question is whether on cosmic scales the deviation from homogeneity is small enough that it may be neglected, to first approximation, for the purpose of modelling cosmological evolution.

The standard model of cosmology assumes that this is the case, and studies structure formation as a perturbation about a homogeneous background spacetime.

Given that the standard model of cosmology faces some issues related to dark energy/cosmological constant (and possibly related issues such as cosmic inflation or dark matter), it has been suggested that these may be but an artifact of the overly idealistic approximation of cosmic homogeneity, and that a more accurate inhomogeneous cosmology would not need to assume any dark energy (e.g. Buchert 07, Buchert 11, Buchert-Rasanen 11, also Scharf 13).

A seminal argument that it is consistent to neglect cosmic inhomogeneity due to (Green-Wald 10, Green-Wald 13), has been called into question in Buchert et al. 15, where it is concluded that the question is more subtle and remains open. Recent review is in Belejko-Korzyński 16.

 

[Ken G]

Danielsson himself writes about the issue discussed here:

U. Danielsson: "Is string theory in crisis?" (July 8, 2018)

An interesting article to be sure, he raises the interesting point that the death of de Sitter vacuums in string theory might come with a rather nice side benefit: the death of the landscape of potential solutions in favor of a special type of solution that actually does permit a de Sitter vacuum in some unseen corner of string theory that would now have a reason to be favored over all the rest (including a violation of the cosmological principle, like perching our universe on the edge of a bubble). This new way of thinking about alternatives to the "landscape" might seem optimistic, but maybe it's just natural hopefulness. But I did take issue with this part: "It is not at all true that string theory cannot be tested. Its first test, which we thought was easy to pass, is to accommodate the accelerated expansion of the universe. "
I actually think Danielsson is misapplying the concept of a "test of a theory," in a way that is becoming pretty common among theorists. A test of a theory must work like this: you first suggest the theory, then you suggest the observation which should only come out a certain way if the theory is good, and then you do the observation, which then either falsifies or favors the theory. That's a test! It is not a test to already know the observation, and sift through a mass of potential theories until you find one that fits the observation. This is certainly a valid way to come up with new theories, but it's no kind of test and cannot be used to claim that a theory is testable. If one cannot suggest a test that actually fits the definition of a test, then the theory is indeed untestable.

 

[Urs Schreiber]

Not sure how this is on-topic, but just to reply:

It is not a test to already know the observation, and sift through a mass of potential theories until you find one that fits the observation.

Not potential theories, but parameters of a theory. See the FAQ How do physical theories generally make predictions anyway?

 

[Ken G]

Not sure how this is on-topic, but just to reply:
Not potential theories, but parameters of a theory. See the FAQ How do physical theories generally make predictions anyway?

Wow, there's a lot of confusion about what a prediction is, and what a parameter is! From that link: "But the point is that once this model has been postulated, then one can use the theory to see what it predicts about the remaining parameters, such as here the fluctuations of the cosmic microwave background radiation in a universe described by this model." I'm afraid you just can't have it both ways-- either you have a prediction, or you have a parameter you are adjusting in a model. Never both at the same time, that's my whole point.

It's on topic because we are talking about to what extent can what string theory likes, or doesn't like, to do is or is not a "prediction" about how the universe works. If string theory is flexible enough to do anything we might later observe, then we can hardly call any of that a "prediction" of string theory, even though we do see language like that surprisingly often (some people even think string theory "predicts" the landscape!). Danielsson was saying that if string theory turns out to not be so flexible, in that it has a hard time with dark energy, that might actually be a good thing-- because now we have leverage to distinguish between types of string theory, perhaps looking for something non-homogeneous or some other selective agent. That's all fine-- until there is confusion about what is a prediction of a theory, versus what is a constraint we are using to hone the version of the theory we will settle on. Those are two completely different things. What is claimed now is that string theory predicts that whatever it is capable of doing should be happening somewhere, yet anything that string theory finds hard to do must be a useful way to constrain string theories. So which is it, are we looking for ways to falsify string theory, or are we married to always interpreting everything that happens in terms of some sort of string theory? We can do either, but we cannot pretend we are doing both-- the former is about testing theories, the latter is about creating theories from the possibilities.

When creationists are asked, "what observational outcome could cause you to reject creationism?", they never have a good answer, which tells us that creationism isn't science. So it is clear that string theorists must also have a ready answer to that question. If a string theorist didn't know about the accelerated expansion, but did know that string theory doesn't do de Sitter well, why wouldn't they say "if the universe if found to be accelerating, that would lead me to reject string theory"? Indeed, Danielsson actually said that it would "test" string theory if it could accommodate acceleration, simply because we already see the acceleration. But tests are never a posteriori like that, a prediction is by definition a priori.

 

[Urs Schreiber]

Today Wrase has the article out, which seems to be about research reported on at StringPheno18 (#26):

• Roupec, Wrase, "de Sitter extrema and the Swampland" (arXiv:1807.09538)

In conclusion (section 5), they review the problem...

"...we have spelled out the problematic details of these [type II dS vacua]. Here two points are particularly important: 1) All dS critical points that have been found up to date involve intersecting O-planes and therefore one cannot solve the ten dimensionally equations of motion pointwise but only after integration over the internal space. 2) The existing critical points were all found numerically and they have not been shown to exist in a large volume and weak coupling regime, for properly quantized fluxes. Here we have taken first steps towards checking point 2)."

But then they find it's hard:

"Unfortunately, these symmetries and the flux quantization conditions are model dependent and need to be worked out carefullyfor each model, which we leave to the future. We restricted ourselves to identifying oneuniversal rescaling that allowed us to rescale the tadpole condition..."

and all they have in the end is this:

"Based on these results we believe that these dS critical points deserve further study because they might provide the simplest explicit string theory setups that carry the potential of falsifying the dS swampland conjecture."

and then a curious final sentence:

"Another, potentially more complicated goal, would be to reach an agreement within our community on the consistency or potential shortcomings of the existing quantum dS vacua scenarios like KKLT [2] and LVS [3]."

 

[Urs Schreiber]

Also the slides from StringPheno18 are available by now. Those by Thomas van Riet are useful:

• Thomas van Riet, Is dS space in the Swampland? (pdf slides)

He also comments on de Sitter holography, which was brought up in #10 above.

 

[Urs Schreiber]

Now in Scientific American:

• Clara Moskowitz, String Theory May Create Far Fewer Universes Than Thought, Scientific American, July 30, 2018

 

[Ken G]

Maybe someone can explain to me how the fact that string theory allows for many universes in any way suggests that those universes exist, or that the fine-tuning problem is solved. We've always had that way of explaining things, long before string theory. Even Einstein could have had a Big Bang with any parameters he needed to explain what we see. So why wouldn't Einstein simply say that all those Big Bangs occurred somewhere, giving a multiverse and no fine tuning problem? And that "multiverse" would have been just as unobservable as the one of string theory. I don't get it at all, why does anyone think that's science?

For example, in the Scientific American article, it is suggested that the multiverse of string theory is just like the many stars of our galaxy, explaining how the Earth is at the perfect distance from the Sun via a random selection effect. The article doesn't even mention the very obvious fact that we can actually see those other stars, making the analogy completely terrible from the perspective of how science actually works! It's like the whole community has, en masse, completely forgotten the scientific method. Even that most basic concept, that of a "prediction of science," gets pretty mutilated in these articles, because a prediction must look like a consequence of a theory that you have not yet seen which you then go out and find-- not something you have already seen that you find your theory can accommodate. The latter is something nice, but it should certainly not be called a prediction, unless, apparently, you are a mathematical physicist.

 

[Haelfix]

Ken G, the explanation you are looking for has been explained many times over the years, but you seem intent on turning this into ridiculous philosophy rhetoric instead of actually learning what people are doing (which is perfectly in the scientific tradition):

The state of string theory is very analogous to what the state of GR was, except that we don’t understand which particular stress energy configuration pinpoints the real world. So go back to the state of things in 1918, long before the FRW solutions had been found.

You have a unique theory... we know what things should look like in the low energy world, we seek solutions of the theory that outputs this state. Currently we get many classes of solutions that get certain features right (gauge groups, number of particle generations etc) but others seem to come out wrong (masses, value of the CC). The parameters here are analogous to the parameter K in FRW. Namely you can’t get anything you want, they’re fixed but can take discrete values that have to be matched to the real world (configurations that sometimes correspond to experiments at very high energies which can’t be currently performed). The big difference is that in GR the real world approximately corresponds to a very simple solution with a high degree of symmetry (but note that it’s not completely exact, no one knows the exact solution of our world in GR, or even bothers to look for it). There is nothing like that currently known in string theory, but it doesn’t mean they shouldn’t keep looking or even understanding the solutions that don’t correspond to the real world (just like in GR)

As for the multiverse, that question can already be answered at the classical level, no need to bring in string theory. In other words, if you have a philosophy objection, first square it against the classical scenario before complicating it with a currently incomplete quantum gravity program.

 

[Urs Schreiber]

To add to that: The reason that some people like to relate the idea of "having different sectors of the universe with different physical constants" ("multiverse") to string theory but not to other theories is that in string theory all would-be constants are actually dynamical fields, so that this idea makes sense in the first place.

 

[haushofer]

Maybe someone can explain to me how the fact that string theory allows for many universes in any way suggests that those universes exist, or that the fine-tuning problem is solved. We've always had that way of explaining things, long before string theory. Even Einstein could have had a Big Bang with any parameters he needed to explain what we see. So why wouldn't Einstein simply say that all those Big Bangs occurred somewhere, giving a multiverse and no fine tuning problem? And that "multiverse" would have been just as unobservable as the one of string theory. I don't get it at all, why does anyone think that's science?

For example, in the Scientific American article, it is suggested that the multiverse of string theory is just like the many stars of our galaxy, explaining how the Earth is at the perfect distance from the Sun via a random selection effect. The article doesn't even mention the very obvious fact that we can actually see those other stars, making the analogy completely terrible from the perspective of how science actually works! It's like the whole community has, en masse, completely forgotten the scientific method. Even that most basic concept, that of a "prediction of science," gets pretty mutilated in these articles, because a prediction must look like a consequence of a theory that you have not yet seen which you then go out and find-- not something you have already seen that you find your theory can accommodate. The latter is something nice, but it should certainly not be called a prediction, unless, apparently, you are a mathematical physicist.

I think the multiverse from string theory is a remnant of the desire for string theory to produce one single, unique theory by some dynamical process singling out 1 vacuum. Since such a process is still lacking, people applied some sort of cognitive dissonance and tried to give all the other vacua an ontological status.

Why not consider quantum field theory in the form of Yang Mills theory, with all possible gauge groups, generations and Higgs fields, and interpret every possible theory as describing an actual universe? Just because it's lacking gravity?

I'm not an opponent of a multiverse, as long as it is suggested by some dynamics, as e.g. in certain inflationary scenario's. If these scenario's are confirmed by observation and they naturally imply multiple causally disconnected regions of spacetime to be created, it'something to take serious. But I've never seen such a motivation for string theory.

 

[haushofer]

Urs, is there a conceptual reason why string theory seems to abhor de Sitter? I know SUSY is not easily reconciled with de Sitter, but I only know of a technical reason (involving the Jacobi identities of the SUSY algebra), but is there also some stringy element to it?

 

[Urs Schreiber]

Why not consider quantum field theory in the form of Yang Mills theory, with all possible gauge groups, generations and Higgs fields, and interpret every possible theory as describing an actual universe? Just because it's lacking gravity?

Because the gauge group etc. in Yang-Mills is an by-hand-fixed parameter, not a dynamical observable of the theory.

 

[Urs Schreiber]

Urs, is there a conceptual reason why string theory seems to abhor de Sitter?

One will have to be careful with these statements. Just because one handwavy argument is wrong doesn't allow one to conclude much beyond the need for better analysis. But check out the discussion is on pages 4 onwards in

• Edward Witten, Quantum gravity in de Sitter space (arXiv:0106109)

and also

• Arvind Rajaraman, de Sitter Space is Unstable in Quantum Gravity, Phys. Rev. D 94, 125025 (2016) (arXiv:1608.07237)

 

[haushofer]

Because the gauge group etc. in Yang-Mills is an by-hand-fixed parameter, not a dynamical observable of the theory.

I see that, but if parameters/moduli are dynamically determined instead of hand-fixed, what exactly makes it more plausible that they correspond to different "universes" which are actually realized?

Thanks for the references, I'll check them out and come back if I'm still puzzled! :)

 

[Urs Schreiber]

what exactly makes it more plausible that they correspond to different "universes" which are actually realized?

I think what is important, since it's a solid fact, is that it makes it possible. From here on, people tell campfire stories (campfire stories with arXiv numbers! :-).

The currently popular campfire story goes like this: If it is possible, it will happen once there is a mechanism that explores all possibilities. One such mechanism might be cosmic inflation, if thought of in the naive way as a small "bubble" (as they like to say these days) of spacetime within a larger ambient spacetime suddenly expanding rapidly. The campfire crowd imagines that each such bubble has a chance to go off with different values of those fields that fix the would-be "constants of nature".

That's fun as a campfire story, but it's not more than that. I wish people would focus more on actually figuring out stuff.

It is ridiculous that we don't even know for sure how much of the apparent cosmological constant deduced from supernova data is actually due to the observable universe not really being completely homogeneous, as assumed in the concordance model. The "backreaction debate" remains inconclusive. This is amazing, it means that potentially we are in for a much larger drama than the disappearance of the KKLT fatansy. Somebody should figure this out. But of course that's much harder than telling campfire stories.

 

[atyy]

It is ridiculous that we don't even know for sure how much of the apparent cosmological constant deduced from supernova data is actually due to the observable universe not really being completely homogeneous, as assumed in the concordance model. The "backreaction debate" remains inconclusive. This is amazing, it means that potentially we are in for a much larger drama than the disappearance of the KKLT fatansy. Somebody should figure this out. But of course that's much harder than telling campfire stories.

That is interesting! I knew about Green-Wald, but didn't know their conclusion was not universally accepted.

 

[Urs Schreiber]

That is interesting! I knew about Green-Wald, but didn't know their conclusion was not universally accepted.

I am not an expert on this, would love to hear your opinion if you know more.

My understanding is that nobody doubts their mathematical conclusion, but that people feel at a loss understanding how their assumptions/axioms are related to the actual problem of inhomogeneity.

In addition, there seem to be numerical simulations that prove that inhomoheneity may have anything between small and large effects (here). Of course there will be assumptions going into that, too...

 

[Ken G]

Ken G, the explanation you are looking for has been explained many times over the years, but you seem intent on turning this into ridiculous philosophy rhetoric instead of actually learning what people are doing (which is perfectly in the scientific tradition):

What is "ridiculous" is to suggest that I am the one bringing basic issues in scientific pedagogy into this thread. Much of the thread, dating back to the OP, has been about the role of mathematical rigor in science ("If at the next social gathering smalltalk with your colleagues you need a good argument that physics does need mathematically airtight proof after all, you’ll have a monumental example here." ) That is quite clearly an issue for scientific pedagogy-- i.e., philosophy. Also, the articles cited in the thread are rife with philosophical statements (a random example from Danielsson: "We therefore think that the most natural assumption, at this point in time, is that string theory conspires against the existence of dS space." Is it not perfectly obvious that talking about what people "think is the most natural assuption" is an example of philosophical thinking?) So no, I did not bring philosophy into the thread, it was already there. I just want it to reasonably reflect proven scientific pedagogy, and to reign in the more glaring variances from that.

It seems to me this thread is about two things: a technical question about whether or not string theory supports dS vacua, and a more widely accessible scientific issue about what are the ramifications if it is or is not supportive of dS vacua. The quote by Danielsson above actually goes so far as to suggest, quite clearly by his choice of language, that if string theory disallows dS vacua, that we should actually look for cosmologies that don't involve dS vacua-- not that we should look for a different physical theory. That's philosophy, and demonstrating a rather complete marriage to string theory thinking.

The state of string theory is very analogous to what the state of GR was, except that we don’t understand which particular stress energy configuration pinpoints the real world. So go back to the state of things in 1918, long before the FRW solutions had been found.

This more or less proves my point actually, the very fact that you think string theory today is at all analogous to GR in 1918. That comparison reflects a departure from sound scientific pedagogy, because although we presently cannot rule out the possibility that string theory might someday explain pre-existing observations that no other theory can explain (like GR could do in 1918 in reference to Mercury's orbit), proper scientific pedagogy calls on us to notice that it has not yet done so. Also, it calls on us to notice the difference between making a prediction that was only later observed (as GR did with the eclipse of 1918), and what people call "predictions" of string theory (like the dubious "landscape", which is no kind of prediction at all, regardless of whether you think it is mathematically sound or unsound). There is no question that string theory is a remarkable theory with great promise, but there is no need to forget what science is in order to praise string theory.

The parameters here are analogous to the parameter K in FRW. Namely you can’t get anything you want, they’re fixed but can take discrete values that have to be matched to the real world (configurations that sometimes correspond to experiments at very high energies which can’t be currently performed).

Yes, that is the natural status of theories, we use observations to fix the free parameters, and then we try to extrapolate beyond what we already know by expecting predictions to come from it-- like how you can use Newton's laws to predict the return of Halley's comet.

As for the multiverse, that question can already be answered at the classical level, no need to bring in string theory. In other words, if you have a philosophy objection, first square it against the classical scenario before complicating it with a currently incomplete quantum gravity program.

I have no problem with people applying philosophy to string theory. My issue is when they pretend they aren't.

 

[haushofer]

I find the introductorion on Danielsson's site https://ulfdanielsson.com/is-string-theory-in-crisis/ ,

"String theory is not in crisis – on the contrary – but string theorists are. The theory refuses to adopt to human preconceptions, and the ruling paradigm since the turn of the millennium is questioned."

curious. The problem of imo is the fact that string theory is a paradigm, and paradigms can't be falsified directly, only certain models/theories in a paradigm. And in string theory we still don't have such theories which reproduce all the phenomena we now describe with the standard model and GR. What I read in the quote above, is a strong believe that the theory will guide us. But to what?

 

[Urs Schreiber]

The problem of imo is the fact that string theory is a paradigm

No. Perturbative string theory is a well defined theory. Non-perturbative string theory is an open problem.

The precise rules of the game are this:

• Find 2-dimensional superconformal field theories of central charge 15 (also known as perturbative string vacua), whose string perturbation series mimics, at low energy, the S-matrix of some perturbative QFT on some desired spacetime background. Here: on asymptotic de Sitter spacetimes.

While well defined, this is extremely hard, since the space of all 2d SCFTs is so very little understood. Hence people resort to 1001 approximations, and that's the source of all the uncertainty and debate.

One of the approximate ideas is that it should be possible to build 2d SCFTs by a "sigma-model"-prescription (these are the "geometric vacua"). For these it may be argued that the effective target space background is a solution to some supergravity theory. Very few sigma-models in curved spacetime are fully understood (essentially only the WZW models), but, still, what is known about sigma-model 2d CFTs is much more than about about "non-geometric vacua" such as Gepner models.

But, unfortunately, general theorems about supergravity seem to rule out de Sitter vacua for these. This means that if there is a perturbative string de Sitter vacuum, then it is not a "geometric" one, coming from a plain sigma-model.

Indeed, all candidate string de Sitter vacua that have been proposed involve "stringy effects" such as O-planes and non-BPS D-branes, which have, ultimately, only an algebraic definition on the level of 2d SCFTs.

In principle it is a well-defined mathematical problem to ask if the space of 2d SCFTs of central charge 15 contains any elements whose low energy effective S-matrix describes scattering on asymptotic de Sitter backgrounds.

The trouble is that actually solving this mathematical problem is technically so utterly out of reach for the time being, that instead of this actual technical problem a huge story of interlocking plausibility arguments is being discussed.

Eventually. the only way to make real progress, will be in developing better mathematical tools and devices to actually study perturbative string theory.

Once that it accomplished (maybe in a century from now?!) we can really check whether there are any perturbative de Sitter vacua.

Then the next question is if this result, either way, will receive corrections from non-perturbative string theory, also known as M-theory. A theory still to be developed. (Incidentally, the titles and abstracts for the contributed talks at the upcoming conference "Higher Structures in M-theory" are now available http://www.maths.dur.ac.uk/lmsreg/php/talks.php?uid=109).

 

[Ken G]

In principle it is a well-defined mathematical problem to ask if the space of 2d SCFTs of central charge 15 contains any elements whose low energy effective S-matrix describes scattering on asymptotic de Sitter backgrounds.

Now that sounds an awful lot like a paradigm to me, in the sense haushofer seems to mean, and not a "single theory" that could be falsified by observation. For example, you have not claimed to know that any such theory even exists, so you can hardly call it a "well defined theory" if it turns out that no such theory exists. Worse, if it turns out that a vast number of such theories could exist, then you can also not call it a well defined theory, as it might still have enough power to describe anything. That has always been the problem, has it not? The problem is, it's a paradigm, not a falsifiable theory, despite the claims to the contrary.

Eventually. the only way to make real progress, will be in developing better mathematical tools and devices to actually study perturbative string theory.

And this is the main point you are making, which seems perfectly valid, but does not require embuing string theory with pedagogical attributes that it simply does not, as yet, exhibit.

Then the next question is if this result, either way, will receive corrections from non-perturbative string theory, also known as M-theory. A theory still to be developed. (Incidentally, the titles and abstracts for the contributed talks at the upcoming conference "Higher Structures in M-theory" are now available http://www.maths.dur.ac.uk/lmsreg/php/talks.php?uid=109).

So what we actually have is, a paradigm suggested to make corrections to another paradigm. That's what we've got, let's not pretend the situation is otherwise. I'm not saying it isn't promising, I'm saying it is being misrepresented by a lot of the language we see. Indeed, if you think that the main problem with the landscape is that it is not a mathematically rigorous (or even a mathematically plausible) application of string theory, others could equally point out that it might suffer from the even more serious problem of not being science at all, but instead, a form of mathematical philosophy (and bad mathematics at that, as you point out). Where your comments are most expert are around the actual mathematical questions, so I laud the efforts you are making to make these more accessible to others. This is a great service to everyone, and a fascinating thread that I have learned a lot from. It seems to me that one way to frame this entire thread is with this question:

If we are to say that string theory is a predictive way of thinking about the nature of things, then is it fair to say that the prediction it makes is there cannot be dark energy? If it does not make that prediction, it sure sounds like a paradigm that can be hammered into any shape we need. And if it does make that prediction, then are we not already on a path that could falsify it before it even gets going? That's the double-edged sword of science: to be good, it has to be capable of being wrong.

 

[Urs Schreiber]

Ken G, that's all right, I know your attitude and I have seen what you can provide, you don't have to keep repeating. I suggest you start a fresh thread on the points that are of concern to you, so that we can keep this thread here focused.

 

[Ken G]

But focused on which part of what you have already said, the mathematics part, or the philosophy parts, that you put into your OP?

 

[haushofer]

No. Perturbative string theory is a well defined theory. Non-perturbative string theory is an open problem.

The precise rules of the game are this:

• Find 2-dimensional superconformal field theories of central charge 15 (also known as perturbative string vacua), whose string perturbation series mimics, at low energy, the S-matrix of some perturbative QFT on some desired spacetime background. Here: on asymptotic de Sitter spacetimes.

While well defined, this is extremely hard, since the space of all 2d SCFTs is so very little understood. Hence people resort to 1001 approximations, and that's the source of all the uncertainty and debate.

Maybe this is semantics, but it depends on what you call a theory and a paradigm. I don't consider perturbative string theory as a different theory from string theory; in my view, perturbative string theory is merely a calculational limitation of string theory. From that point of view I say we don't have the precise rules.