What is the Connection Between String Theory and Stability?

[marcus]

A new book by Lawrence Krauss is scheduled to appear in bookstores tomorrow. Has anybody here seen an advanced copy?

Peter Woit has a review of the book
http://www.math.columbia.edu/~woit/wordpress/?p=281

One of the perks of having a popular blog website seems to be that publishers send you reviewer copies of new books, before they hit the stores and go on amazon.

Here is the amazon page


It has a bunch of shorter reviews and the usual amazon info.

Krauss has written a number of general audience physics and cosmology books, including for instance a popular one called The Physics of Star Trek

This new one has the intriguing title:

HIDING IN THE MIRROR: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond

Part of the idea of the book is to explore mankind's age-old fascination with the notion of unseen extra dimensions.

 

[Vast]

Having read "Beyond Star Trek: From Alien Invasions to the End of Time" and "The Physics of Star Trek", Lawrence Krauss reveals some of the mistakes that come up throughout the popular television series. Although not in a negative way, in fact I’ve learned a bit from those two books. If they’re anything to judge by, I would say this new book is worth the read also. Of particular interest is the connection between extra dimensions and an age old cultural fascinations with the idea.

 

[selfAdjoint]

I just preordered the new Krauss book, based on what I read on Woit's site. It was interesting to read some of the comments there on the comparison of Krauss's version of brane worlds to Lisa Randall's treatment in her new book Warped Passages. I thought that Lubos' comment that Krauss has never done any work in that field, whereas Randall has her name on a major initiative, does have some merit, although it was expressed in Lubos' usual over-the-top in-your-face style. I'm planning to go to a talk Randall is giving in Appleton next January, and if she is signing copies of her book I wil buy it then.

BTW, Hiding in the Mirror and Warped Passages sound like new volumes in some Sword and Sorcery series by Robert Jordan or Terry Goodkind!

 

[marcus]

A new book by Lawrence Krauss is scheduled to appear in bookstores tomorrow. Has anybody here seen an advanced copy?
Peter Woit has a review of the book
http://www.math.columbia.edu/~woit/wordpress/?p=281
...Here is the amazon page

...
Krauss has written a number of general audience physics and cosmology books, including for instance a popular one called The Physics of Star Trek
This new one has the intriguing title:
HIDING IN THE MIRROR: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond
Part of the idea of the book is to explore mankind's age-old fascination with the notion of unseen extra dimensions.

MSNBC had a blog-review of Krauss new book:

http://www.msnbc.msn.com/id/9787346/#051025a

Here is an interview with Krauss in the Cleveland Plain Dealer
http://www.cleveland.com/books/index.ssf?/books/more/transcript.html

if that link doesn't work try
http://www.cleveland.com/entertainment/plaindealer/index.ssf?/base/entertainment/112990140131420.xml&coll=2

the MSNBC inhouse blog that provided part of this information is run by
Alan Boyle and is called COSMIC LOG
http://www.msnbc.msn.com/id/3217961/

it might be something to check out from time to time. While reading about Larry Krauss book I happened on a beautiful picture of a black hole gobbling up stars and a link to this ESO press release:

http://www.eso.org/outreach/press-rel/pr-2005/phot-33-05.html

You may have seen this picture elsewhere. the article is called
Feeding the Monster
New VLT Images Reveal the Surroundings of a Super-massive Black Hole

kind of telescope photo that hooks one into a lifelong love-affair with astronomy

 

[selfAdjoint]

I don't know why they were privileged, but my local Barnes and Nobles has had Hiding in the Mirror for a week. I was able to read comparable sections from it and Warped Passages last Thursday. Just as advertised, Kraus is more succinct, Randall more discursive, but both of them taught me things I didn't know. When my bank account will stand it I will buy both. Well actually I'm waiting to see if Randall is selling her book at her talks (she's on tour now). If so I will buy Passages when she comes to Appleton in January.

 

[notevenwrong]

One of the perks of having a popular blog website seems to be that publishers send you reviewer copies of new books, before they hit the stores and go on amazon.

Unfortunately that's not the case. Although I think it would be a great idea if publishers sent me review copies of new books, that hasn't been happening. Here's my secret: at the Strand bookstore here in New York, they have on sale review copies they got from people who did get them, and bring them into sell. So, at the Strand you can get copies of most new books a week or more before they actually appear in the bookstore.

 

[marcus]

.. Here's my secret: at the Strand bookstore here in New York,..

Big Apple perk

I used to live in lowereastside, 12th st.
know the unionsquare neighborhood and those bookstores somewhat

 

[marcus]

Lawrence Krauss, whose new book is out, has been invited by the group blog COSMIC VARIANCE to be their guest blogger.
http://cosmicvariance.com/2005/11/14/our-first-guest-blogger-lawrence-krauss/

this just happened today, he wrote a short essay to start the thread---about string theory, about aesthetics and hype-vs-empiricism issues, about the current science/religion skirmishing.

AFAIK the guest blog just went up and there are some half a dozen comments. Nothing special so far but to keep an eye on.

 

[marcus]

Here is the amazon page for Krauss HIDING IN THE MIRROR


Before the book came out, Peter Woit did a very helpful job of sifting out some key quotations
http://www.math.columbia.edu/~woit/wordpress/?p=281
---------quotes from Krauss and others exerpted in Peter Woit's review------
But in the ever-optimistic string worldview, there are no embarassments… For these ‘true believers’, every new development provides an opportunity to confirm one’s expectations that these ideas ultimately reflect reality.

… string theory might instead do for observational cosmology what it has thus far done for experimental elementary particle physics: namely, nothing.

In short, the as-of-yet hypothetical world of hidden extra dimensions had, for many who called themselved physicists, ultimately become more compelling than the world of our experience.

This embarassment is solved in the way other similar confusing aspects of string theory and M-theory are sometimes dealt with: Namely, it is assumed that when we fully understand the ultimate theory, everything will become clear.

Over the past five years, hundreds if not thousands, of scientific papers have been written considering cosmological possibilities that might be associated with Braneworld scenarios. One cannot do justice to all of them, but the greatest justice I could probably do to many of them is to not mention them here.

What the notion of large or possibly infinite extra dimensions has done is borrow some of the facets of string theory while ignoring the bulk of the theory (forgive the pun), about which, as I have explained, we have only the vaguest notions. It seems to me to be a very big long shot that an apparently ad hoc choice of what to keep and what to ignore will capture the essential physics of our universe.

This [the Landscape] has resulted in yet another fascinating sociological metamorphosis of the theory, with warts becoming beauty marks.

… the anthropic principle is something that physicists play around with when they don’t have any fundamental theory to work with, and they drop it like a hot potato if they find one.

This finally brings up back to M-theory. Faced with the prospect that the theory may ultimately predict a virtually uncountable set of possible universes, some string theorists did a 180-degree about-face. Instead of heralding a unique Theory of Everything that could produce calculable predictions, they are now resorting to what even a decade ago they may have called the last refuge of scoundrels. But, when string theorists take a position, they do it with flair.

…if the landscape turns out to be the main physical implication of the grand edifice of string theory or M-theory… we might be left with the mere suggestion that anything goes. What was touted twenty years ago as a Theory of Everything would then instead have turned quite literally into a Theory of Nothing.

Krauss ends his book with an epilogue describing conversations with Gross, Wilczek and Witten about string theory. Wilczek is a skeptic, annoyed by the excessive claims made for the theory. Witten is quoted as saying that string theory “is a remarkably simple way of getting a rough draft of particle physics unified with gravity. There are, however, uncomfortably many ways to reach such a rough draft, and it is frustratingly difficult to get a second draft.” He justifies work on string theory partly through progress it has led to in the understanding of strongly coupled gauge theories.

Gross is described as convinced "that the theory is simply too beautiful not to be true”, an attitude that strikes Krauss “as sounding like religion more than science.” With this, Krauss ends his book by quoting Hermann Weyl:

"My work always tried to unite the true and the beautiful, but when I had to choose one or the other, I usually chose the beautiful."

and concludes:

So it is that mathematicians, poets, writers, and artists almost always choose beauty over truth. Scientists, alas, do not have this luxury, and can only hope that we do not have to make this choice.
-----end quote from Woit's review----

 

[marcus]

Lawrence Krauss, whose new book is out, has been invited by the group blog COSMIC VARIANCE to be their guest blogger.
http://cosmicvariance.com/2005/11/14/our-first-guest-blogger-lawrence-krauss/
this just happened today, he wrote a short essay to start the thread---about string theory, about aesthetics and hype-vs-empiricism issues, about the current science/religion skirmishing.
AFAIK the guest blog just went up and there are some half a dozen comments. Nothing special so far but to keep an eye on.

there are now over 20 comments on the thread, #17 is by Lee Smolin

Lee Smolin on Nov 14th, 2005 at 6:17 pm
Hi,

I agree with most of what Lawrence said. But since I was mentioned, I should clarify why I and most people who work on quantum gravity, apart from string theorists, find it impossible to agree with Sean’s statement that string theory is “by far our current best idea” about quantum gravity.

-Any acceptable quantum theory of gravity must incorporate the basic lesson of GR that the geometry of spacetime is dynamical and defined without reference to any fixed background-hence background independent. String theory has as yet no such formulation. Furthermore, there are several theories that provide precisely such a theory, such as loop quantum gravity, spin foam models and dynamical triangulation models, about which many non-trivial results have been proven.

- Even at the background dependent level GR is not recovered because all backgrounds on which consistent propagation of worldsheets have been shown are static in that they have timelike or null killing fields. So, there is no evidence that string theory exists even on backgrounds that are time dependent, which is the generic case in GR. We know that the Einstein equations on the target space are (up to higher order terms) a necessary condition for consistent worldsheet propagation. But sufficient conditions include also canceling the tachyon instability. In all known cases this imposes another condition which is worldsheet supersymmetry (or something equivalent) which in turn requires that the background be static. So it is not true that string theory predicts or incorporates GR as a low energy limit, because all solutionis to GR seem to be ruled out as giving inconsistent propagation except static ones.

Thus, while there is talk about string theory on time dependent backgrounds there are no actual examples. Given the importance of supersymmetry in consistent string dynamics, it is plausible to me that this is because there is only consistent worldsheet propagation on static backgrounds.

-The precise matching of black hole thermodynamics to string states is impressive but only seems to work for special black holes that have positive specific heat (and are hence near extremal.) This is because no black holes are involved at all, instead what is counted are states of non-gravitational systems of branes in flat space with gravity turned off that have, by virtue of BPS symmetry the same quantum numbers of certain positive specific heat black holes. This can’t work for negative specific heat black holes because they are not BPS and because they can’t have the same thermodynamics of orindary systems with positive specific heat. There is no evidence string theory can describe precisely generic negative specific heat black holes. I suspect this may be because there is no consistent worldsheet propagation on backgrounds with horizons-because they do not have global timelike killing fields.

-On top of this, while there is very non-trivial evidence for all orders finiteness, it is still not proved (please don’t jump on me again about this unless you have a new paper with a full proof.)

-Since Sean’s statement is comparative, it is important to say that background independent approaches exist, and many key results have been shown about them. LQG, in its spin foam formulation, continues to advance and is now, in my view, the “best model.” There were recently big advances on the hardest problem, that of getting known physics form the low energy limit announced in talks by Rovelli, Freidel, Markopoulou and others at the loops05 meeting (now with talks on line at http://loops05.aei.mpg.de/) , and there were predictions for corrections to the CMB described in the talk there by Hofmann. Elimination of both black hole and cosmological singularities has recently been shown in related models. This is on top of proofs of uv finiteness and the fact that the theory is background independent. Black hole entropy is understood for real negative specific heat black with real horizons.

In my view the second best model is the Loll-Ambjorn causal dynamical triangulations model, with stunning recent progress described by Loll at loops05.

If string theory overcomes the problems mentioned I would be the first to cheer But for the present I believe that the background independent appraoches are moving faster and are more worthy of our time.

Thanks,

Lee

 

[marcus]

there are now over 133 comments on the thread, #133 is again by Smolin

133. Lee Smolin on Nov 17th, 2005 at 9:55 pm
Dear Moshe,

Thanks for your last remark. Perhaps I can ask my question about time dependent backgrounds in the following, hopefully constructive way: You say, “the way Einstein equations are derived in string theory is that you expand around the most general (weakly curved) background, and the conditions for consistency of the string propagation, without any further input, yield the Einstein equation for that background… The background is the most general one, one never has to specify that it is static”

Here is my understanding (and please correct me if I am wrong.) What you described is certainly the whole story for the bosonic string. But that has tachyons, and so could not describe the excitations of a stable ground state. So we have to impose additional conditions to cancel the tachyon to find a worldsheet theory that could descrive the excitations of a stable ground state. So here is my question: Are we sure that the extra conditions required to cancel the tachyon do not restrict the possible vacua to a small set of solutions of the Einstein’s equations ?

My worry is that the answer is yes. My evidence for the worry is that in many cases the cancelation is accomplished by supersymmetry and, as I argued before, supersymmetry implies, by the closure of the algebra on the Hamiltonian, that the background has a timelike or null killing field.

There may be exceptions to this, but am I wrong to say that there are many cases that work like this? If not, I conclude that in these cases it is not true that the acceptable backgrounds are generic solutions to the Einstein’s equations, because they must have killing fields. So my understanding is that while we can claim by the argument you made that generic weakly curved solutions to the Einstein equations are predictions of bosonic string theory, the same is not the case for supersymmetric string theory.

Now, might there be other ways to cancel the tachyon leaving stilll generic weakly curved solutions to Einstein’s as good string backgrounds? My understanding is that a few examples have been explored, such as linear dilatons, coset constructions etc. but that either there was still a static metric (Einstein or string frame) or there were unresolved issues of instabilities. Is this right?

Now, please tell me 1) Is there anything wrong with this argument? 2) Among the possible time dependent backgrounds that have been explored, which is the best case? 3) Even if there were shown to be a few consistent time dependent backgrounds, wouldn’t this still be a long way from what we want, which is showing that they are generic, which is what we have to have to claim that the generic solutions to Einstein equations are predictions of superstring theory.

Thanks,

Lee

Besides #17 and #133, Lee has posted a couple of other comments (#41 and #63, if you want to look for them)
the poster called Moshe has responded once to Smolin, that i could find, which was #50. It may be that what Lee means by "thanks for your last remark" was this Moshe post #50-----I couldn't find anything else it could refer to.

What impresses me here? Carefullness of statement and courtesy of address. Smolin is clearly trying to see if it is possible to have a constructive and substantitive discussion in public where non-experts can "look over the players' shoulders" or listen in. but there is a lot of distraction. If there COULD be an open constructive polite public discussion, where non-experts could listen, that would be great. Smolin said something about that as a goal. he's obviously interested in having that. However my impression is it's "noisy" at Cosmic Variance. Actually, in my humble opinion, there'v been quieter more substantive discussions between Smolin and other string experts over at Woit's Not Even Wrong blog.

Come to think of it, since Peter woit is not a partisan of either Loop or String he may preside over a better blog for really educational discussions. At Cosmic Variance the management is potentially more biased because involved in string research (and NOT in loop)----whereas Peter is involved in neither. But we just have to keep an open mind and see how this occasion turns out.

Anyway what we have at the moment is a small give and take exchange (around 3 or 4 posts in the midst of over 100) about a key issue----almost lost amongst other discussion---the other discussion could be enlightening as well. But this issue is really a key one. in what sense, if at all, does the string framework reproduce gravity in a mutable background---where space geometry changes with time

I wonder if Moshe will post a reply any time soon? If he does I will copy it here and we can take a look

 

[marcus]

indeed the poster at Cosmic Variance called Moshe did reply quite promptly and at considerable length. I will copy his response in full

------quote-----
137. Moshe on Nov 18th, 2005 at 12:28 am
Hi Lee, thanks for your last comment, it is certainly a pleasure talking physics!
(and apologies for the technical level of this stream of comments, but this is the most efficient way to resolve technical issues).

So, here is my understanding of the situation. The issue is that of classical stability, whether or not the spectrum of linearized fluctuations around specific background has tachyons. Now if space is exactly flat, the bosonic string has a tachyon with string scale mass, which means instability with string timescale. With worldsheet SUSY this disaster is avoided, one gets spectrum with no (classical linearized) instabilities.

Now, let us talk about backgrounds that are almost flat, then just by continuity the only thing one has to worry about is the spectrum of modes that would have been zero modes in flat space. So my statement is that weakly curved solutions of string theory have tachyons if and only if the corresponding GR+matter solution is stable. So string theory at the classical level is as stable or unstable as the corresponding field theory it includes. On the classical level such instability is not such a disaster, one simply gets an unstable solution of Einstein equation, those are fine, they are not inconsistent (nor are they very interesting…)

The point about worlsheet SUSY is a red herring I believe. Generally worldsheet structures are invisible from the spacetime viewpoint, they are just mathematical tricks (it is unnecessarily confusing to think about string worldsheet as embedded in spacetime, as one has to sum over worldsheet metrics, where the induced metric from spacetime is only one of the metrics to be summed over). Worldsheet SUSY is that mathematical trick allowing spacetime fields to have spin. It turns out that in string theory it also projects out the bosonic string tachyon, leaving the situation I described in the last paragraph. So all the set of models we mentioned, orbifolds, cosets etc. are consistent backgrounds of classical string theory with no tachyons.

So to summarize,classically I think the statement that generic weakly curved solution of Einstein equation lifts to a classical solution of the full superstring theory, with no tachyons.

I keep adding the adjectives “classical” and “weakly coupled” to everything, and at that level I think what I said so far is correct, hopefully someone will correct me if I am wrong. Now once we add quantum corrections there are several disasters that can happen, for example w/o spacetime SUSY various massless modes will start getting sources, so static solutions of the classical equations will no longer stay static (which sometimes is referred to as “instability”). If you are not interested specifically in static solutions maybe this point is not such a concern.

More seriously for time dependent backgrounds, I think singularity theorems say that in many cases (generically?) time dependent backgrounds will tend to have spacelike singularity in the past or future, and then the background is no longer weakly curved everywhere. This manifest itself by certain singularities in string theory observables, also sometimes referred to as “instabilities” (one can detect certain lack of imagination…). As I said this is the reason why this is an interesting topic. It is certainly not clear that a generic classical solution of any theory, especially containing gravity, should lift to a full solution of the quantum theory. The question which do and which do not, and whether one can do it perturbatively or not, are very interesting open issues, not a lot is known about them currently.
best,

Moshe
----endquote---

 

[marcus]

the preceding post was Moshe's #137 over at cosmic variance.
Lee just replied (it was #154) and then Moshe again:

----quote from CV---
Lee Smolin on Nov 20th, 2005 at 6:13 pm

Dear Moshe,

Thanks very much for your #137. This is helpful, but can I query you on one point, where you say that on “…backgrounds that are almost flat, then just by continuity the only thing one has to worry about is the spectrum of modes that would have been zero modes in flat space. So my statement is that weakly curved solutions of string theory have tachyons if and only if the corresponding GR+matter solution is stable. So string theory at the classical level is as stable or unstable as the corresponding field theory it includes.”

Can you fill in a few details of this argument? It seems to me that given that the cancellation of the tachyon involves a projection to a smaller state space (the GSO projection) and given that the projection implies spacetime supersymmetry which is broken as soon as there is any time dependence, you have to show that you can continue to impose a projection that eliminates a tachyon for any small non-supersymmetric deformation of the background geometry. Has this been done? If not, I don’t think you can use an effective field theory argument that assumes that the tachyon is absent from the deformed theory.

On a related point, you say, “It is certainly not clear that a generic classical solution of any theory, especially containing gravity, should lift to a full solution of the quantum theory.” But for the classical theory to be recovered as the low energy limit, must it not be that every solution to the classical theory that is weakly curved on the Planck scale must lift to a coherent state in the quantum theory?

Thanks, Lee

=======================
Moshe on Nov 20th, 2005 at 6:38 pm

Hi Lee,

Back to physics, very theraputic…

The comment of continuity was just an intuitive comment, not really necessarily an EFT argument. Basically the spectrum of the string is continuous as a function of the background fields (w/o changing the GSO projection), so string scale tachyon cannot just pop up when you turn on arbitrarily small background fields. In any event, I assure you there are also more complete calculations, that was just an argument why this had to be the case. Incidentally, even for static backgrounds there are non-SUSY classically stable cases, but they are quantum mechanically unstable in the sense that they don’t stay static after including quantum corrections.

As for the last paragraph, I mentioned that in the context of backgrounds which develope singularities, and then we don’t have a criteria for judging which background lift to the full quantum theory. My bet is that weakly curved backgrounds should be fine, but one cannot know for sure yet. (incidentally, is it always true that for time dependent background singularity thm. dictate there generaically exists future or past singulairty?)

best,

Moshe

==============
Moshe on Nov 20th, 2005 at 6:56 pm

Oh, one more point, the GSO projection by itself does not imply spacetime SUSY, it just allows for that possibility, if the background fields cooperate…

----end quote---