The write-up of Larry McLerran’s summary talk at Quark Matter 2006 has now appeared. This talk created a bit of a stir since McLerran was rather critical of the way string theorists have been overhyping the application of string theory to heavy-ion collisions.
McLerran explains in the last section of his paper the main problem, that N=4 supersymmetric Yang-Mills is a quite different theory than QCD, listing the ways in which they differ, then going on to write:
Even in lowest order strong coupling computations it is very speculative to make relationships between this theory and QCD, because of the above. It is much more difficult to relate non-leading computations to QCD… The AdS/CFT correspondence is probably best thought of as a discovery tool with limited resolving power. An example is the eta/s computation. The discovery of the bound on eta/s could be argued to be verified by an independent argument, as a consequence of the deBroglie wavelength of particles becoming of the order of mean free paths. It is a theoretical discovery but its direct applicability to heavy ion collisions remains to be shown.
McLerran goes on to make a more general and positive point about this situation:
The advocates of the AdS/CFT correspondence are shameless enthusiasts, and this is not a bad thing. Any theoretical physicist who is not, is surely in the wrong field. Such enthusiasm will hopefully be balanced by commensurate skepticism.
I think he’s got it about right: shameless enthusiasm has a legitimate place in science (as long as it’s not too shameless), but it needs to be counterbalanced by an equal degree of skeptical thinking. If shameless enthusiasts are going to hawk their wares in public, the public needs to hear an equal amount of informed skepticism.
Another shamelessly enthusiastic string theorist, Barton Zwiebach, has been giving a series of promotional lectures at CERN entitled String Theory For Pedestrians, which have been covered over at the Resonaances blog.
Zwiebach’s lectures are on-line (both transparencies and video), and included much shameless enthusiasm for the claims about AdS/CFT and heavy-ion physics that McLerran discusses. His last talk includes similar shameless enthusiasm for studying the Landscape and trying to get particle physics out of it. He describes intersecting D-brane models, making much of the fact that, after many years of effort, people finally managed to construct contrived (his language, not mine, see page 346 of his undergraduate textbook) models that reproduce the Standard Model gauge groups and choices of particle representations. Besides the highly contrived nature of these models, one problem with this is that it’s not even clear one wants to reproduce the SM particle structure. Ideally one would like to get a slightly different structure, predicting new particles that would be visible at higher energies such as will become available at the LHC. Zwiebach does admit that these contrived constructions don’t even begin to deal with supersymmetry-breaking and particle masses, leaving all particles massless.
He describes himself as not at all pessimistic about the problems created by the Landscape, with the possibility that there are vast numbers of models that agree to within experimental accuracy with everything we can measure, thus making it unclear how to predict anything, as only “somewhat disappointing”. He expects that, with input from the LHC and Cosmology, within 10 years we’ll have “fully realistic” unified string theory models of particle physics.
The video of his last talk ran out in the middle, just as he was starting to denounce my book and Lee Smolin’s, saying that he had to discuss LQG for “sociological” reasons, making clear that he thought there wasn’t a scientific reason to talk about it. I can’t tell how the talk ended; the blogger at Resonaances makes a mysterious comment about honey…
Finally, it seems that tomorrow across town at Rockefeller University, Dorian Devins will be moderating a discussion of Beyond the Facts in Sciences: Theory, Speculation, Hyperbole, Distortion. It looks like the main topic is shameless enthusiasm amongst life sciences researchers, with one of the panelists the philosopher Harry Frankfurt, author of the recent best-selling book with a title that many newspapers refused to print.
Update: Lubos brings us the news that he’s sure the video of the Zwiebach lectures was “cut off by whackos” who wanted to suppress Zwiebach’s explanation of what is wrong with LQG.
Update: CERN has put up the remaining few minutes of the Zwiebach video.
I am not saying that everything is solved in intersecting brane worlds and I would agree that they are only understood as long as susy is unbroken. But if you say that all particles are massless you should say the same about the all the fermions in the standard model. Only the Higgs has a genuine mass terms.
But just as in the standard model, there are yukawa type couplings between the higgs and the fermions in intersecting brane worlds. Once the Higgs takes a vev (and this is allowed by the equations of motion) the fermions are massive.
It is one of the features of intersecting brane worlds that left and right handed fermions and the higgs all live at different intersections of pairs of stacks of branes and there is a triangle of branes which has these three particles living at its corner. You can stretch a (euclidean) string (instanton) over this triangle and this gives the yukawa coupling in the low energy theory proportional to exp of minus the area of this triangle. As the families are supposed to arise from multiple intersections of the stacks as they wrap around the torus where all this is living, triangles of roughly equal geometric area give rise to exponentially different yukawa couplings, a feature many find attractive.
You can say many things about why intersecting brane worlds are not realistic (susy, loads of scalars from bulk moduli) but the mass pattern is one of the pros of these models.
“String Theory for Pedestrians”
I suppose this is a typically post-modernist reference to “Lie Groups for Pedestrians”, the semi-famous and mega-annoying book by Harry Lipkin. I remember thinking the title offensive, did not regard myself as any kind of pedestrian, and didn’t need a boy scout to escort me across the street of math-physics to the far curb of understanding. I think that book was the beginning of the end of my positive attitude about modern mathematics and its practitioners. Instead I decided to learn from fellow pedestrians Lie and Klein.
-drl
Looking through the transparencies, one finds the following typical example of sophistry in action:
The String Theory Landscape
String theory shares with Einstein’s gravity a
problematic feature.
Einstein’s equations of gravitation admit many
cosmological solutions. Each solution represents a
consistent universe, but only one of them represents our observable universe.
Hmm, the last time I checked, this is just an initial-boundary value problem for a set of differential equations combined with a set of massively iffy assumptions about the early conditions in the Universe. What this has to do with the metaphysical ethos of the string landscape is beyond my pedestrian ability to understand. Hey! what did I just step in? TAXI!!
-drl
But that’s precisely what that “landscape” is: a space of solutions to something generalizing Einstein’s equations.
Urs,
That’s great news. Perhaps you can let us know exactly what the equations are that generalize G=8piT so we can use them to make predictions about the results of experiments.
A string vacuum is a certain 2dCFT. “Geometric string vacua” describing 2dCFTs that can be written as sigma-models are determined by what is called the “string background field equations”, which are something like Einstein-Dilaton-Maxwell gravity with various other fields — like those infanmous “fluxes” — and various higher correction terms.
In principle, the “landscape” is the space of solutions of these field equations.
Like in any KK-like theory, physics in 4d is sdetermined by how these solutions look like in the compact directions. There are many such solutions, hence many ways to have physics in 4d.
urs,
From your description, it appears to me that not only do you not know what the exact equations in question are, but you don’t even know what exactly what space the equations live on. Perhaps, instead of just telling us that the equations that determine a string background are called the “string background field equations”, you could write them out explicitly, or point us to somewhere where this has already been done.
Hey Peter,
Urs is spewing nonsense, but your sneering attitude towards him in the last few posts can’t help but remind me of Clifford’s attitude towards you in his “tempest” posts.
The man,
Thanks for the good advice.
I do get frustrated by the continuing mystification that surrounds the issue of the current state of attempts to get unified particle physics out of string theory. Opinions can reasonably differ about hopes for the future, but the question of what is now known about string theory ground states is a straight-forward one, and string theorists should stop “spewing nonsense” on the subject.
Asking questions for clarification is not sneering. Clifford, Lubos and Jacques certainly attack because they can’t psychologically face string theory’s failure as physics.
If you want to see real sneering, ask one of those string theorists about alternatives like Smolin’s work.
Another “test of string theory” paper appearing on PRL, by Gary Shui et al. This time, it’s using CMB data to measure the geometry of compact dimensions.
z3,
See my comment about this week’s “test of string theory” in the other thread.
Has anyone read this article?
http://www.ccnmag.com/news.php?id=4789
Sounds very promising!
You actually make a very good point about the “mystification” issue.
As far as string theory is concerned, if you ask for something with actual equations, they’d give you a long list of big (and expensive) books to read and then suggest no one would understand them anyway unless they take 5-10 years courses in somewhere like Harvard (and it works, I’m still curious about what’s so special there in string theory math).
So my question still remains: is there any single (self contained) book (or whatever) with equations, say something like 500+ pages that would explain what’s in Greene’s book with actual equations? There’s been many suggestions, but buying them all would surely be waste of money..
No, it wouldn’t be a waste of money from the perspective of the authors of those books. You can’t have too much learning…
Ari,
I haven’t actually seen the book, but from its table of contents the new Becker-Becker-Schwarz book sounds like the closest thing to what you are looking for. It is 700 pages of difficult material, and really understanding this is definitely a multi-year project. Then there’s the problem that the book doesn’t actually seem to really explain how bad and generic the problems of this research program are, or that any contact with experiment is at best far in the future, at a time-scale that is receding into the distance…
“It should be said at the outset that, as of yet, there has been no experimental verification of string theory. Also, no sharp prediction has been derived from string theory that could help us decide if string theory is correct.”
Quote from Zwiebach’s book (chapter 1.3 right at the beginning).
This seems very reasonable to me and in stark contrast with say Kaku’s claim that one could prove string theory using only pure mathematics.
The part I’ve seen from his lecture at CERN follows the same spirit as this quote from the book.
About this CMB test of string theory, first of all you need sensitive enough data. Let’s suppose you have this. Doesn’t the article assume there are extra dimensions in the first place? Obviously you can come up with another explanation for the CMB patterns which don’t assume extra dimensions. Plus, let’s suppose you narrow down the possibilities of geometries with the data. If the resulting 4D physics (at low energies) doesn’t match what we observe, then there’s a piece of evidence falsifying string theory.
‘If the resulting 4D physics (at low energies) doesn’t match what we observe, then there’s a piece of evidence falsifying string theory.’
But string theorists can take all falsification to be a mere ‘anomaly’, as they already do with failures of string theory already (supersymmetry falsely suggests a really massive cosmological constant, for example). Science doesn’t come from experimental disagreement, because the theory gets modified, just as general relativity getting a small positive CC in 1998 to fit observations:
‘Scientists have thick skins. They do not abandon a theory merely because facts contradict it. They normally either invent some rescue hypothesis to explain what they then call a mere anomaly or, if they cannot explain the anomaly, they ignore it, and direct their attention to other problems. Note that scientists talk about anomalies, recalcitrant instances, not refutations. History of science, of course, is full of accounts of how crucial experiments allegedly killed theories. But such accounts are fabricated long after the theory had been abandoned. … What really count are dramatic, unexpected, stunning predictions: a few of them are enough to tilt the balance; where theory lags behind the facts, we are dealing with miserable degenerating research programmes. Now, how do scientific revolutions come about? If we have two rival research programmes, and one is progressing while the other is degenerating, scientists tend to join the progressive programme. This is the rationale of scientific revolutions. … Criticism is not a Popperian quick kill, by refutation. Important criticism is always constructive: there is no refutation without a better theory. Kuhn is wrong in thinking that scientific revolutions are sudden, irrational changes in vision. The history of science refutes both Popper and Kuhn: on close inspection both Popperian crucial experiments and Kuhnian revolutions turn out to be myths: what normally happens is that progressive research programmes replace degenerating ones.’
– Imre Lakatos, ‘Science and Pseudo-Science’, pages 96-102 of Godfrey Vesey (editor), ‘Philosophy in the Open’, Open University Press, Milton Keynes, 1974.
In case anybody is really interested in how to compute corrections to G=8pi T here is what you have to do: Write down the sigma model for a string propagating in an arbitrary background geometry given in terms of G,B and phi (let’s take RR fluxes to be 0 for the moment or use Berkovitz’ formalism). Then do a world sheet loop computation (i.e. expansion in alpha’ which plays the role of hbar in that theory) of the beta functions (in terms of G, B, and phi). For any order of alpha’ this is a well defined procedure and there is no arbitrariness. Then you get the background equations of motion by requiring the beta functions to vanish. This is explained in detail in GSW Ch. 3.4 at the one loop level (i.e. the first alpha’ correction) and has been computed if I am not mistaken up to four loops.
This should answer your question of how string theory generalised the Einstein equation. I described a perturbative computation but this is not any worse than elsewhere in particle physics.
Robert,
The problem with the perturbative calculation you suggest is that it doesn’t lead to something realistic with broken supersymmetry and stabilized moduli. For this you need non-perturbative phenomena: where are branes in your calculation?
This is the difference between string theory and standard QFTs used in particle physics. In string theory the perturbative ground state doesn’t give you what you want, so you make some assumptions about what possible ground states may come out of the full theory, ending up with an incredibly complex set of possibilities. In the Standard Model, the electroweak ground state is exactly the unique perturbative one, which you understand well, and for the QCD ground state you have a well-defined non-perturbative theory that you can use to calculate numerically what it is, and get a unique answer.
What if you didn’t know how to formulate QCD non-perturbatively, perturbative QCD didn’t correspond to anything observed, and people went around claiming that non-perturbative QCD, whatever it was, led to a huge number of different possible ground states, so many that you couldn’t use the theory to predict anything. Would anyone take this seriously?
I really “liked” this comment of Lubos’s, in reference to Zwiebach’s lectures:
The goals of high-energy theorists have always been, are, and will be much more ambitious and abstract than a particular dirty experiment, whether or not an unrefined and uncultural observer of science likes it or not. Barton’s focus only reflects the experimental character of the location where he gave the lecture.
The problem is not that string theory disagrees with a particular dirty experiment, but that it disagrees with pretty much every dirty experiment, to the extent that it says something about reality at all.
I realize that I might sometimes sound wacky, but in one respect I am very conservative: I simply don’t think that disagreement with experiment is a good thing.
I hope it’s clear that “liked” = ROTFL!
Andy, sorry!
Thomas, no problem. It’s hard to be nuanced on a blog.
much more ambitious and abstract than a particular dirty experiment,
Delubosional… 🙂
Huh?
“cheap porn for undemanding consumers”
People have complained that the book is too hard for the average reader, maybe I should get the publisher to put the above blurb from Lubos on the back cover.
Peter, I don’t understand your reply. I fail to see how the choice of vacuum influences this beta function calculation which is in some sense local at a point on the world-sheet. It is one way to obtain the low energy field equations and all discussions of KKLT etc of the many vacua actually talk about the _solutions_ of these equations. There is little doubt about the equations.
I had thought the standard line of attack here would have been to mention that the corrections are alpha’ corrections and are thus important only if center of mass momenta get close to the Planck scale and are thus unlikely to observe in the real world soon. Which is followed by a philosophical discussion if this theory is really a different theory from GR from which it doesn’t differ at everyday energies.
Robert,
You can choose any background you want and try and do perturbative string theory on it, but string theorists keep telling us that string theory is a unique theory with no adjustable parameters. The theory is supposed to tell us what the possible lowest energy (or metastable) states of the theory are. Doing this requires a full non-perturbative string theory, and no one knows what this is.
That might be.
But, by definition, the “landscape” of string theory is the space of “perturbative vacua” which, in string theory, is a space of certain 2d CFTs. For a subset of these (the geometrical ones), this space is the space of solutions of a generalization of Einstein’s equations.
DRL’s quote, which got this discussion started, is therefore accurate in the realm of perturbative string theory.
Urs,
The “landscape” of string theory is supposed to be the set of all vacuum states (or metastable states) of string theory, this is what is physically relevant. Again, you can’t actually know what this set is until you have a non-perturbative string theory.
Peter, you are moving the goal posts. The question was
I gave you the answer and now you complain that I did not answer the different question “What are the vacua of string theory?”. The corrections to Einstein’s equations can be computed without knowing the answer to the second question.
Robert,
These are questions about physics, so what I was asking for is something that answers a question about physics. I don’t doubt that you can write down equations that no one knows how to connect to physics, I’m claiming you can’t write down equations that answer physical questions.
In particular, I don’t believe that, from string theory, without knowing which vacuum state we’re in you can write down a universal modification of Einstein’s equations. Without knowing the vacuum state you don’t even know how many large dimensions there are or what the string coupling is.
As Lisa Randall once pointed out: “sure, string theory predicts GR… in 10 dimensions”.
Since it seems we are arguing about a definition, let’s look at the literature to see what people actually do when they say they study the “landscape”.
The review
Fux Compactifications
http://arxiv.org/abs/hep-th/0610102
by Douglas and Kachru might help.
They go through lots of examples, write down the generalized Einstein actions of string theory background fields and find the solutions to their equations of motions.
For instance take the first example, p. 29. The generalized Einstein-Hilbert action of relevance is equation (36), the ansatz for solving its equations of motion (finding its extrema) starts in equation (41).
You can search for “Einstein equations”.
They also do discuss (p. 4) that invoking “nonperturbative effects” is one aspect done in this business, but necessarily so. So if you don’t believe in these nonperturbative effects there is still a lot of ordinary landscape remaining.
Finally, maybe one comment: unfortunately this review does seem to take that as granted, but it might be worth pointing it out: the very reason for calling these solutions to the string background equations — which, recall, determine conformal sigma-models — “vacua” is that given any such 2-dimension CFT in perturbative string theory we imagine regarding its n-genus correlators to be the n-loop amplitudes of a perturbative expansion of something about that very “vacuum”.
urs,
The equation you point to has an undefined term in it that the authors call “S_loc” which they don’t specify other than to say that this is where you can put in things like D-branes and orientifold-planes. A non-perturbative theory is ultimately required to know what consistent choices can be made for such terms, as well as to understand whether these equations actually correspond to a valid approximate calculation in a ground (or metastable) state of the theory.
I’d think D-branes and orientifold planes would still be part of the perturbative landscape, in that they are captured just by looking at 2-dimensional CFT: backgrounds with these features still correspond to points in the space of 2-dimensional superconformal QFTs with central charge 15.
But I do completely agree that whenever some author invokes aspects of “nonperturbative string theory” it might at best be a well-motivated guess.
I also agree that it might be that perturbative string theory is phenomenologically unviable, that there is no hope to get reasonable physics from studying the “perturbative landscape”, i.e. the space of c=15 2d SCFTs. Might be.
All I wanted to say is that the “perturbative landscape” of string theory — despite its silly name and the fact that we have no good real understanding of it at all and no matter how much we trust its prospects regarding phenomenology — is a well defined mathematical entity — and that many points in this space do indeed correspond to solutions of (natural) generalizations of Einstein’s equations.
The number of large dimensions or the value of the coupling constant are properties of the solutions to these equations not of the equations. And these equations definitely hold outside the branes in the bulk. And this equation is easy to check: just create some Planck scale curvature using some mass/energy distribution, and measure the graviational (and other) fields. Then you can check if they obey these alpha’ corrected equations. This should be independent of the vacuum you select at infinity. And if the coupling (in terms of the dilaton) is not too big, non-perturbative corrections should as well be controlable (being of order e^-1/g or smaller).
Robert,
So, your modification of Einstein’s equations depends on which ground state you’re in, but knowing what these ground states actually are depends on knowing what non-perturbative string theory is (which you don’t).
What people are talking about often when they talk about a”string theory background” is some sort of semi-classical approximate ground state built on a specific 10d geometry, adding branes, fluxes, etc. The problem is, without knowing the underlying non-perturbative theory, you don’t know how well these reflect an actual ground state of the theory. You can argue that for special regions of parameter space you expect the semi-classical approximation to be good, but generically there’s no reason to expect this.
So, the equations you are trying to sell as analogous to G=8piT come in an infinite number of sets of equations, you don’t know what space parametrizes this infinite number, and whatever it is, on most of it these equations reflect an approximation which is probably no good and has nothing to do with physics.
I still think there’s a problem with the analogy of solutions in GR and string backgrounds….
So, your modification of Einstein’s equations depends on which ground state you’re in, but knowing what these ground states actually are depends on knowing what non-perturbative string theory is (which you don’t).
How exactly did you go from what Robert said to that?
Aaron,
Actually this discussion has gone far from the original origin which was Urs’s claim that the Landscape is just like solutions to G=8piT.
As for what I wrote, is it or is it not true that the modification of Einstein’s equation in string theory depends on the background (i.e. ground state)?
In the perturbative string? No. The condition is just that the sigma model be conformal. You write down a general sigma model and write down the beta-functions. It’s done in Polchinski I.3.7, for example.
And the beta functions one gets are, incidentally, for strings in pure gravitational and dilaton backgrounds, those used by Perelman to complete Hamilton’s program of solving the Poincaré conjecture.
Aaron,
I know the argument in Polchinski, which deal with backgrounds large compared to the string scale. My question is whether this holds once you introduce other structures a la KKLT to stabilize the moduli.
The perturbative string should properly be thought of as giving equations on the set of 2D QFTs of which sigma-models are only a part. The solutions to these equations are the 2D CFTs. (This is background independent on the classical level. To do background-independent quantization is trickier.)
When you start talking about moduli stabilization, however, one is talking about the 4D effective theory. This, by necessity, depends on the choice of compactification. Nonetheless, the theory is what you get from compactifying the string theory equations on your choice of CY. The final issue is the question of nonperturbative corrections. These are dealt with on a somewhat ad hoc basis in string theory because we a nonperturbative formulation of string theory in general. These do depend on the choice of background, ie, solution to the equations of motion. But this isn’t particularly different than how one deals with instantons in ordinary QFT.
Is Lorentz invariance optional in any of the known approaches to string theory? J. Distler’s paper implies that Lorentz invariance (among other things) is a necessary attribute of string theory, or at least of what he calls “canonical string theory”, whereas others seem to argue that string theory could be pursued in a non-Lorentz-invariant context. Can anyone clarify this? Does the “landscape” of possible string theories include some in which Lorentz invariance does not hold?
A related question: Is the “landscape” outside of what Distler calls “canonical string theory”? If so, at what point would the “landscape” become canonized?
“and that many points in this space do indeed correspond to solutions of (natural) generalizations of Einstein’s equations.”
Urs, what do you mean by ‘natural’?
On the one hand, nothing deep. I just added this remark to indicate to those who didn’t know it that its not a bunch of weird generalizations in all kind of silly directions, but just the natural kind that you would expect: everything remains generally covariant, with various fields (p-forms, spinors, etc) all appearing coupled to GR in terms of scalar invariants cooked up from covariant derivatives.
While I think there is a also a deeper sense in which the string background equations are “natural”, this is here not the place to discuss that. Suffice it to say that these generalizations are not chosen by hand but all appear automatically from an underlying principle. And not just in string theory #.
Urs, while I agree with your notion of naturalness you should not forget to point out that the naturalness is of the form of the equations but there are numerical coefficients for which a range of values would be natural but which get specific values in string theory. How many of them there are depends of course on the symmetries you assume your theory to have (for example N=8 susy fixing a lot of relations).