The String Vacuum Project, described as “a large, multi-institution, interdisciplinary collaboration”, that has been established over the last few years, is having its Kick-Off Meeting next month at the University of Arizona. This group had submitted grant proposals to the NSF for funding of such a project in the past, but I don’t know if they ever managed to get NSF or other funding. They motivate the project by claiming that

Given that relatively large numbers of string vacua exist, it is imperative that string phenomenologists confront this issue head-on…

In this context “relatively large” involves numbers like 10^{500}, 10^{1500}, etc.

Bert Schellekens has a web-site devoted to promoting the Anthropic Landscape, where he argues that

The String Theory Landscape is one of the most important and least appreciated discoveries of the last decades.

Besides the web-site, he has slides from two general talks on-line (here and here). In the talks he compares string theorists to the famous Emperor parading in no clothes, except what he is criticizing is those string theorists who have been unwilling to acknowledge the existence and importance of the anthropic landscape. He’s critical in particular of

those people claiming that they have always known that String Theory would never predict the standard model uniquely, but that they did not think this point was worth mentioning.

His modernized version of the fable of the Emperor goes as follows:

Many years ago, there lived some physicists who cared much about the uniqueness of their theories. One day they heard from two swindlers that they could make the finest theory which was absolutely unique. This uniqueness, they said, also had the special capability that it was invisible to anyone who was stupid enough to accept anthropic thinking.

Of course, all the townspeople wildly praised the magnificent unique theory, afraid to admit that anthropic thoughts were inevitable, until Lenny Susskind shouted:

“String theory has an anthropic landscape”

It’s not clear who he would identify as the “two swindlers”….

According to Schellekens, the “string vacuum revolution” is on a par with the other string theory revolutions, but most people prefer to overlook it, since it has been a “slow revolution”, taking from 1986-2006. The earliest indications he finds is in Andy Strominger’s 1986 paper “Calabi-Yau manifolds with Torsion”, where he writes:

All predictive power seems to have been lost.

and in one of his own papers from 1986 where the existence of 10^{1500} different compactifications is pointed out.

Schellekens claims that “string theory has never looked better”, but he completely ignores the main question here, the one identified by Strominger in 1986 right at the beginning. If all predictive power is lost, your theory is worthless and no longer science. What anthropic landscape proponents like him need to do is to show that Strominger was wrong; that while string theory seems to have lost all predictive power, this is a mistake and there really is some way to calculate something that will give a solid, testable prediction of the theory. The String Vacuum Project is an attempt to do this, but there is no evidence beyond wishful thinking that it can lead to a real prediction. Schellekens has worked on producing lots of vacua and describing them in a “String Vacuum Markup Language”, and in his slides describes one construction that involves 45761187347637742772 possibilities. These possibilities can be analyzed to see if they contain the SM gauge groups and known particle representations, but this is a small number of discrete constraints and there is no problem to satisfy them. The problem is that one typically gets lots and lots of other stuff, and while one would like to use this to predict beyond-the-SM phenomena, there is no way to do this due to the astronomically large number of possibilities.

He lists goals for the future (“Explore unknown regions of the landscape”, “Establish the likelihood of SM features”, “Convince ourselves that the standard model is a plausible vacuum”), but none of these constitutes anything like a conventional scientific prediction that would allow one to test to see if what one is doing has any relation to reality. In the end, he comes up with the only real argument for the String Vacuum Project and other landscape research, that of wishful thinking:

… and maybe we get lucky.

**Update**: There’s a story about the String Vacuum Project in this week’s Nature by Geoff Brumfiel. It includes skeptical comments from Seiberg and yours truly, as well as Gordon Kane’s claim that:

evidence supporting string theory could emerge “within a few weeks” of the [LHC]’s start-up.

**Update**: At the blog Evolving Thoughts, there’s a discussion of whether theoretical physicists have now taken up a “stamp-collecting” model of how to do science. I point out that this is stamp-collecting done by people who don’t have any stamps, just some very speculative ideas about what stamps might look like.

The Monster group has nearly 10^54 elements. Creating a multiplication table for the Monster would describe it completely. Such a table would have nearly 10^108 entries, however. Nonetheless, Griess showed *by hand* that the Monster, in fact, is the automorphism group of a 196884-dimensional commutative nonassociative algebra, and many important discoveries involving the Monster followed, despite it’s size. So, who can really say that understanding the Landscape fully will be forever out of reach? It might just need a simple genius move, and if numerical analysis helps finding patterns in the Landscape, let them do it! I attended some seminars on numerical landscape analysis, and the results seem quite nice and sometimes intriguing. And what I’ve understood is that most of the vacua can be easily ruled out and that it seems that only very few Calabi-Yau possess interesting properties (low Betti numbers, etc) to make them good candidates for describing Standard Model.

hv,

One of many problems with your analogy is that the set of elements of the Monster form a finite, simple group, which is an extremely special mathematical structure of a highly symmetric sort. There is simply zero reason other than wishful thinking to believe that anything like this is true of the set of “string vacua”.

The monster as well as string vacua share the property that they both are part of the theory of the “space” of 2-dimensional (rational) conformal field theories. There is every reason to believe that this space is a rich and beautiful mathematical entity in its own right.

The main problem about this space is that it is so very little understood that it seems to be just premature to try to do things like statistics over it. Let alone trying to predict particle masses from it.

Urs,

Besides not knowing what the “space” of 2d CFTs is, the lack of a non-perturbative formulation of string theory means you wouldn’t be able to extract physics from it, even if you knew what it was.

I wouldn’t mind, if I knew what it was.

Part of the beauty of string theory is that it builds on the notion of 2D CFT, which is a mathematical structure of the kind mathemticians get in love with (like the monster) but bigger. And less well understood. (Well, actually for non-super and

rational2-D CFT people have understood a whole lot meanwhile.)If everybody would just stop worrying about cranking out numbers where no numbers can be cranked out and concentrated again on investigating the basics we’d be in much better shape.

The basics of CFT is well understood; there is no more low-hanging fruit to pick. Moreover, beautiful as this mathematical structure may be, it is not the only conceivable mathematical structure.

Cranking out numbers is important to figure out if it is CFT or some other structure that governs the laws of the universe. The simplest numbers are indeed easy enough to crank out, and they disagree with experiment – spacetime does not have 26 or 10 dimensions, and there are not 496 different gauge bosons. CFT number fit perfectly into 2D statmech, but this only shows its limitations. Whereas one may argue about CFTs beauty in hep, in statphys there is no doubt that it only applies to toy models in 2D, and not to the physically important systems in 3D.

One can learn one thing from these toy models, though. Universality in 2D is explained by CFT, i.e. by the Virasoro algebra. Universality is an empirical fact also in 3D. Therefore, one may suspect that 3D universality has a similar explanation as 2D universality.

Thomas Larsson what do you mean by “universality” in your last comment? What does it mean that universality is explained by CFT in 2D and is an empirical fact in 3D?

Universality in statphys means that similar systems do not just have similar, but identical (or completely different) critical exponents. This is explained in CFT because there is only a discrete set of universality classes (unitary Virasoro representations) in the simplest cases. That universality holds also in 3D is standard lore and has been confirmed by experiments (real and numerical) and various theoretical arguments (epsilon expansion and others).

Thanks, but I guess it was too technical for me. Now I don’t know what you mean by systems and their critical exponents.

I guess I want to know what aspect of physical reality “universality” refers to. What kind of experiment could confirm or refute it.

It seems LQG people also becoming fond of landscape-like ideas:

http://arxiv.org/abs/0803.2926

Some coments on this paper:

http://www.physicsforums.com/showthread.php?t=223450

Chris A,

Dienes’ paper implies nothing about the existence of small cosmological constants. Anybody who tries to use samples from a probability distribution to estimate its behavior in the low-probability tail is, as von Neumann would say, living in a state of sin. The only way to learn anything about the low probability tail is either to generate an astronomical number of samples or to use theory, both utterly hopeless at this state of the game.

curious, see this:

http://en.wikipedia.org/wiki/Critical_exponent

Thanks, I’ve got it now. I was aware of various other meanings of the word “universality”, but not of this particular meaning until now.

Thomas Larsson wrote:

Right, we are certainly not talking about low-hanging fruit here.

And the space of 2d CFTs is not low hanging fruit and not well understood. Even the more easily accessible subspaces have only been understood rather recently.

One problem is that what many people call CFT is only half of the story: namely “chiral CFT”. This is given, equivalently, by

– a vertex operator algebra and its representation category

– a conformal net of local algebras on the line and its representation category .

All things Virasoro live here. But that’s not yet a CFT, it just encodes the local symmetry properties of a CFT. In particular, there may be none, one or several non-equivalent full CFTs associated with a given vertex operator algebra.

A full CFT is a representation of the category of conformal 2-dimensional cobordisms such that the infinitesimal neighbourhood of the length 0 cylinder reproduces the given chiral CFT.

In the case that the chiral CFT part is

rationalin that the representation category has finitely many isomorphism classes of simple objects (“primary fields”) the “space” of all corresponding full CFTs is essentially understood: there is one equivalence class of such CFTs per Morita class of special symmetric Frobenius algebra objects internal to the representation category.One may think of that results as “completely solving rational 2d CFT”. But even in that case a problem remains: to connected the Frobenius algebra object with the chiral vertex operator algebra requires a choice of isomorphisms between the vector spaces associated by the Reshitikhin-Turaev functor to given surfaces and the space of conformal blocks of that surface given by the VOA.

That isomorphism is explicitly known only in a few simple cases.

But already at this point, lots of nice structure appears. Practitioners I know think of rational 2d CFT as a generalization of group representation theory.

And the structure of the proof for the result of the rational case indicates what one should expect more generally. So now the question is how to generalize the proof to

– non-rational

and to

– supersymmetric

2dCFTs. It is clear that we expect to see again that these are given by certain Frobenius algebra objects in certain VOA representation categories. But now there are technical details to deal with, since in lots of places where we have finite sums appearing in the rational case, the non-rational case, naively, leads to infinite sums. (Not those kind of infinite sums one sees in perturbative QFT, though.)

Thomas Larsson wrote:

Bosonic 2d CFTs of central charge 26 correspond to effective target spaces which are 26-dimensional manifolds only in a tiny subset of the space of all such CFTs, namely those that are entirely of the naive sigma-model type with large flat dimensions.

Supersymmetric 2d CFTs of central charge 15 correspond to effective target spaces which are 10-dimensional manifolds only in a tiny subset of the space of all such CFTs, namely those that are entirely of the naive sigma-model type with large flat dimensions.

That there is and has been so much focus on such utterly over-simplistic CFTs as string backgrounds is the problem whose very point we are discussing: the space of all CFTs is little understood and everybody has been searching the key under the lamppost which illuminates only the most elementary examples.

Not that it is guaranteed that the key actually is somewhere else in the currently dark realms of CFT-land, but it is certainly premature to make statements about the shape of the key from what we can find under this tiny spotlight.

To appreciate the situation, it may help to simplify it drastically and marvel at how complicated it still is:

As Roggenkamp and Wendland show, and especially Yan Soibelman describes in a big (unfortunately not yet published) opus, a 2dCFT encodes a categorification (2-dimensional version) of a Connes spectral triple. The effective target space described by the CFT regarded as a string background is the spectral geometry encoded by the point particle limit of that spectral triple. So when we are talking about string backgrounds, we are talking about a vast generalization of ordinary spectral (“noncommutative”) geometry, which itself is a vast generalization of ordinary geometry.

Alain Connes picks a certain spectral triple that encodes a target space which is a weird non-commutative space and argues that it comes close to encoding the standard model. Nobody complains that he picks that spectral triple from a huge “landscape”, namely from the space of

allspectral triples. Remarkably, his spectral triple has K-theoretic dimension 10. Suppose this arises as the point-particle limit of a 2-spectral triple a la Soibelman, i.e. from a 2dSCFT of central charge 15. Then, clearly, this won’t be of sigma-model type and will not describe an effective target which is a 10-dimensional manifold.All this mostly shows one thing: we know so shockingly little about the space of all 2dCFTs and yet are used to hearing so shockingly many claims about what it looks like.

So perturbative string theory does not predict that spacetime is 10-dimensional. What it does predict (essentially as its fundamental hypothesis!) is that spacetime is the effective target geometry of a 2dSCFT of central charge 15. That’s all.

10-dimensional manifolds appear here only in the most simple minded examples. Claiming that string theory predicts 10-dimensional spacetime is exactly like claiming that general relativity predicts flat empty Minkowski spacetime. No, it does not. This just happens to be the most simple solution that comes to mind.

Precisely similar comments apply to heterotic models which predict 496 gauge bosons.

“10-dimensional manifolds appear here only in the most simple minded examples.” But those are the models that are uniquely said to be truely superstrings. Or at least that is what seems but taking a daily look at hep-th. Some trolle people even troll to say that those are uniquely the true ones. I mean, that’s the impression I take by looking everywhere…

If some structure is physically relevant, it is usually the simplest examples that are the easiest to see in nature. In the application of CFT to 2D statphys, the simplest examples are things like the Ising and Potts models. One could in principle construct systems with arbitrary multicritical behaviour (e.g. RSOS models), but it is almost impossible to realize such systems experimentally when multi >= 6 or so. Similar comments apply to spin (reps of SO(3)) and to the gauge groups in the SM.

Since the simplest CFTs applied to gravity give completely wrong answers, it is a very clear indication that the basic idea is just wrong. But my opinion is of course colored by the fact that I have successfully unified the symmetry principles underlying gravity (4-diffemorphisms) and QM (lowest-energy reps). The resulting theory does not look anything like string theory.

That mathematicians fall in love with some mathematical structure has historically not been a good indicator of the structure’s physical value. Ptolemy and Lorentz (and definitely Poincare) were good mathematicians by the standards of their time, and they may have fallen in love with circles and classical field theory, respectively. This neither proved epicycles nor ether theory, it only made it take longer before people accepted the experimental verdict.

Replies to Daniel de Franca’s comment are given here.

well, It is not clear why string land scape should be predictive anyway. The best alternative we have to string landscape is a QFT like Standrad model or some extension of it where parameters are anyway put by hand. String theory should be thought as a method of including gravity above the framework of quantum field theory.

But the important problem with String theory is that we have not yet derived Standard Model from string theory and it is not even sure that whether it can at all be done. One may argue that the problem is too easy !!!, as there are many vacuas ( may be 10^O(100)), many of them should reproduce the standard model as we know. However, one should keep in mind that in standard model we have a many parameters (about 20?, can’t remember now) and most of which is known up to many decimal place. It naively seems that we know standard model also in a very huge accuracy. May be number of string vacuas are much more, but reproducing Standard Model will still be an interesting and significant achievement.

Peter said

“The problem is that no one is able to, for any even slightly realistic string theory models, compute the relation between observable quantities (eg masses and mixing angles) and things like moduli parameters that specify the model. This has been the case since string theory became popular, there is no reason to believe it is going to change.”

Can somebody kindly enlight me about the exact reason why mass and mixing angles are not calculable from moduli parameters? May be they can be done numerically with recent advances in numerical constructions of Ricci-flat metric in 3-folds.

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