News From The Front, II

By cjohnson | October 31, 2005 6:45 pm

Well, I suddenly have 45 extra minutes on my hands as I was supposed to be at a very interesting two hour lunch meeting which I’ve now missed. I learned the hard way that we have in addition to the Annenberg School for Communication, the Annenberg Center for Communication, which is of course in a completely different location, North of main campus. I spent half the meeting running around the wrong place trying to find it, and no-one at the School could help me because they did not know anything about it, until after a long time someone had the bright idea of telling me about the existence of the other place….sigh. So I have some time to devote to you, dear Reader, and it will help me calm down from the frustration of it all.

Well, I promised a long time ago (since some of you asked) to tell you what it is that I am working on in my physics research. The problem always was that if I had time to go into a description in the blog, it seemed more appropriate that I should be doing the actual research rather than blogging about it. Time is not easy to find, you see. So sorry that it took so long.

It is hard to start without setting the scene with motivating remarks, so what I am going to do is steal some of my own words from the introduction to the paper I’m writing with my young collaborators James Carlisle (graduating soon with a Ph.D. from Durham, UK) and Jeff Pennington (an undergradaute at USC), and sprinkle in some comments for those who don’t work in this area. Then I’ll do a part III, and maybe even a part IV, to which the mysterious scribblings on the board will be connected.

It is safe to say that, at this point in time, we do not understand string (or M-) theory as well as we would like. While we have understood and appreciated that there is a rich bounty of physical phenomena contained in the theory, this has mostly been uncovered in perturbation theory, occasionally sweetened by a glimpse into the non–perturbative realm afforded by special sectors of the theory such as soliton solutions (including branes of various sorts) or various topological reductions.

(Yes, I really do write this flowery stuff in the introductions to my research papers! I don’t know how my various collaborators have put up with it, but they do, bless ‘em.)

I spent time time describing D-branes here.

The physics that we have so far learned from the theory has provided numerous promising and exciting phenomenological scenarios that form the basis for several research endeavours to understand and incorporate current experimental and observational data from Nature, and furnish testable predictions about new physics. These endeavours are still embryonic, and cannot fully mature without much more understanding of the underlying theory.

In fact, most of what you’ve heard about in various places about the exciting stuff that’s going on in string theory and what it promises for describing Nature are, in my humble opinion, early efforts in the game. Incredibly valuable endeavours….. but only the beginning. See my comments about what I think about some of the current issues here. Be sure to read my comments in the discussion part of that thread too.

Furthermore, much of what we have learned pertains to the critical string theories, a rich class for study of course, but after all of the non-perturbative lessons that we have learned in the last decade, the fact that as a field we mostly still linger in the critical domain should be regarded as nothing more than the force of habit; so much historical baggage.


The “non-perturbative lessons of the last decade” are all those things that people bang on about in the press. The “Second Superstring Revolution” and all that. This is where we learned that other extended objects (branes) are just as important as strings, that all the five string theories in ten dimensions that we thought were different from each other are actually all part of one bigger framework. The framework is called “M-Theory”, and is expected itself to be a powerful dyamical theory in its own right, from which you find string theories as perturbative limits arising from making certain parameters small. The key point of all that is that String Theory Is Not A Theory Of Strings.

Also, “critical” string theory is that thing that people usually just call “string theory”, and this is where you hear all the stuff about it being 10 dimensional, etc, and we have to figure out ways of compactifying six of them to four dimensions, etc. All good stuff. What people never tell you is that it is a complete overstatement to say that string theory can only live in 10 dimensions. This is just wrong. It is that several of the easiest string theories to study live in ten dimensions. You see people found ten dimensions interesting a long time ago, went there, and then forgot that this is not the only choice. Furthermore, they never told the young people they were training about that choice that was made either. So an entire generation (or two) is missing out on a lot of potentially great physics. Amazing, really, but true. Let’s carry on:

Having broken free of the shackles of perturbative thinking, there is no compelling physical reason to restrict attention to critical strings in a search for a description of Nature. It is time to try to move on to other areas of the theory, where the tools and concepts we need to make contact with Nature may well be waiting to be found.

Ok so what have I been up to? I’ve been working in an arena where a lot of the stuff that we consider really important lessons of string theory can be studied cleanly, but in a much more simplified setting. Rather like studying spin systems like the Ising model and its cousins to get insights into phase transitions (condensation, vaporization, etc) in real systems. Let’s carry on (the water gets a bit choppy in the next paragraph or two, but then calms down again):

There has been some movement. Due to progress in the understanding of open string sectors in Liouville conformal field theory, (Techner, Fateev, and the Zamolodchikovs) and following on from the proposal by Verlinde and McGreevy, recent years have seen a growing realisation that the non-critical string theories in two dimensions (or fewer), despite being rather simple as compared to their higher dimensional cousins, contain several model examples of the non-perturbative phenomena that have so fascinated us from higher dimensional critical strings such as D-branes, holography, open-closed transitions, tachyon condensation, etc. In fact, this class of models -first arrived at by double scaling certain matrix models

Stop. This needs some work to explain. Can’t do it now or it will break the flow. “Liouville conformal field theory” is the type of technology one uses to study these non-critical strings. (“Non-critical” strings are the ones that don’t need to live in the (“critical”) 10 dimensions.) Liouville conformal field theory is hard, but there’s been a lot of incremental progress made over the years. But there is an alternative approach using “matrix models”. What are those? Takes time to explain, and I will try another time. Suffice to say that there is a way of studying the dynamics of simple models of large matrices which -after a certain limit called the “double scaling limit”- define for you these non-critical string theories….. we wont’ need that in what we’re to talk about, but see the classic trio of papers here, here and here if you just can’t wait for an explanation. Also, “D-branes, holography, open-closed transitions, tachyon condensation, etc”, if you don’t know in detail what those are, can be just thought of as “some of the modern cool stuff that people are trying to use to describe nature using string theory”. Ok, let’s go back in:

-contains the earliest examples of fully non-perturbative formulations of string theories, which remain the only formulations available where one can ask and answer (appropriate) questions arbitrarily far from perturbation theory. Furthermore, the fact that one can get different string theories by expanding the physics in different small parameters (something we’d like to better understand about M-theory and the critical string theories) is manifest in these models. For example, in one class of models first found and studied extensively in refs.[here I give a ton of references to old papers of mine. Here's one, and another, and another.], and to be further discussed at length in this paper, the physics is contained rather succinctly in a non-linear differential equation, with no reference to strings and their world-sheets. It is only when a small dimensionless parameter is identified and the solution is expanded in terms of this parameter does the physics take on the interpretation of a string theory (where the small parameter is the string coupling) which can be open or closed depending upon which parameter is taken to be small.

I will actually show you how this works, so don’t worry too much about what all that means if it was not clear. Just take away from that the fact that there are really wonderful things we’d like to do -such as define a string theory non-perturbatively without reference to strings, and then recover them in perturbative limits (just like we learned from M-Theory!)- and this is what these models do for you. Since way back in 1990/1991!

The celebrated non-perturbative phenomena mentioned [earlier - the cool stuff] are examples of exciting physics of which we would like even more examples, and of which we would like better understanding. The type of non-perturbative formulations under discussion furnish such examples and enhance our understanding somewhat by sharpening the terms in which the phenomena of interest are expressed and by confirming them as robust (perhaps even generic) non-perturbative features of the theory.

Double scaled matrix models (and their accompanying physics) were abandoned as non-perturbative approaches by the field only a few years after their first construction, the main reasons cited being non-perturbative ambiguities and oversimplicity. This was despite clear demonstrations

…by yours truly and his collaborators so long ago. But nobody would listen. We were just some unknowns in England. (Now I’m unknown in the USA instead :-) )…

that there were fully consistent and unambiguous models available which avoided these objections, and non-perturbative maps between models with closed and open strings.

Now comes the swell in the background music…..

We should be careful to not make the same mistake twice and again turn our attention away from these models prematurely. There is an important question to ask: Now that we have recognised that these models describe so many of our favourite important non-perturbative phenomena, can we learn from them about new non-perturbative physics that has hitherto been overlooked?

More later.

-cvj

CATEGORIZED UNDER: Science
  • http://iso42.blogspot.com Wolfgang

    Clifford, be careful with matrix models and non-critical strings.
    You might end up with dynamical triangulation and then Lubos will go after you …

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Thanks, but I’m puzzled. What have I to fear from Lubos?

    -cvj

  • http://eskesthai.blogspot.com/2005/09/cft-and-tomato-soup-can.html Plato

    So Clifford you work outside of the box then? :) How the heck do you get all that information ever to fit inside that box?

    You have a way don’t you of reducing from a fifth(just outside the box)down to two?

    So realistically to get to the fifth, you needed something did you not to validate this process?

    So you know these generalizations are very simplistic, but for the layman I am if you can supply such proof, then it’s not as if we are all be taken for a ride in terms of ID speculation. At least this is what people are saying.

    It would seem to me, that a person who would continue in this vain would have “other convictions” that might spur one on to hold to the questions of what is happening outside that box.

    While it might indeed be conjurred up in the mathematical abstract, I think it is more then what a gavin might say in regards to particle manifestations and high energy impact having no resolution in the weak field manifestation.

    If the model is consistently built, then what says you do not have a conisstent method right from the weak field, right to the high energy impact and microstate backhole production, might signal from it’s inception?

    While some might of discarded calorimetric validation proceses and say they are irrelevant I think the Smolins and all like minded would be happy to see where this emergent property might avail itself, when indications within those calorimetic measures lead us ever so close to the plank length perspective as a signal from that microstate blackhole.

    Gavin was wrong not to think of Pierre Auger as a sideline to high energy considerations as a viable process within the context of our cosmo logical relations.

    Sorry, It’s all a blur to me.:)

  • http://www.pyracantha.com Pyracantha

    CLifford:

    What you are writing about, would take me more than a lifetime to understand, given that I am currently only working on Newtonian high school physics. So I will ask just one thing: what do you mean by “perturbation” or “(non)perturbative?”

  • Jack

    Thanks, but I’m puzzled. What have I to fear from Lubos?

    The reference is to one of LM’s punch-ups with famous physicists on his blog. In this case Eva Silverstein. Let’s just say that LM doesn’t like non-critical strings. Actually, for once, LM gave as good as he got, so it may be worth your while to search his archive [earlier this year I think]. Or not…..

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Pyracantha. Hi! Sorry I used those terms without explanation….actually I thought that I explained it in the posts that I gave links to. No matter. Roughly it is like this. You have a system you want to solve, and it is hard to do. Difficult to get the numbers out exactly. But sometimes you can make an accurate approximation. Then you might ask “why is this approximation a good one to do?”…”under what circumstances is the discrepancy between my approximation and the exact answer actually a small discrepancy?” “Can I make systematic improvements on the approximation and compute corrections to my approximation and improve it?”. The science of getting useful answers to those questions is called “perturbation theory”, or you are working in a “perturbative regime”. It is usually the case that you have a small paramater that you are expressing your perturbation theory in terms of. An example from Newtonian physics might be the pendulum. You’ve probably studied the “simple pendulum” as it is called, the case of a mass on a light string, swinging back and forth. Look it up in one of your textbooks when you get the chance, as it is a classic. You’ll find that there is the solution to the problem when the amplitudes of the swinging (oscillations) is small is a sinusoidal oscillation. Simple Harmonic motion it is called. Small compared to what? You ask. Good. Small compared to the length of the string. So your small parameter is the ratio of the amplitude, to the string length. Let us call that ratio R. It turns out that the exact solution for this case, the Simple Harmonic Motion, is x(t)=A cos(wt) where A is a number (maximum amplitude), t is time, and w is a number setting the frequency, it depends on the acceleration due to gravity and the pentulum length: w^2=L/g). Now this is an exact and beautiful solution, but it is only an approximation…. but quite an accurate one when x is small. It turns out that there will be slight deviations from this motion if you could measure accruately enough. But you can compute corrections to this motion in a series in R: #1 * R+ #2 * R^2 + #3 * R^3 + …… since R is small and less than 1, these corrections get succesively smaller (#n just means a number)….. this is the essence of perturbation theory. (I’ve done this off the top of my head, so forgive the poor notation and sloppiness that no doubt people will beat me up over…)

    There are times when you don’t have the luxury of a small parameter. Then you might be stuck for a way to get the right answer. Let’s say that you had some good reason to want to compute the motion of your pendulum for really large swings….. Then the Simple Harmonic Motion (A cos (wt)) is no use to you. You have to try something else. Unexpected physics may be lurking in the non-perturbative regime.

    Same for string theory. We can say all sorts of wonderful thing about strings -and gosh darn it, they are wonderful – but most of that arises from working in a perturbative limit. What is the small parameter? The “string coupling”. What’s that? a parameter that measures how strongly the string interacts with each other in a process. They interact by splitting and joining, and the likelyhood of that is given by this number, usually denoted g_s. One of the thigns we’ve learn in recent times that that the physics get really rather more interesting when g_s is not small. In fact, one of things that happens is that the strings interact so strongly with themselves that they are no longer recognisable as strings anymore…. the whole description of the physics in terms of interacting strings is itself an artefact of perturbation theory and we have to throw it out. It is as though -to really screw with the analogy- when you set your pendulum swinging really large swings, you found that not only was it not doing harmonic motion, but it wasn’t a pendulum any more either!

    Turns out that is what Nature is asking us to do with string theory. To a first approximation, strings seem to have a good shot at describing things we like, such as gravity, particles of various sorts….. we’re excited. But Nature tells us that some of the harder things we need to address with strings -things which will tell us whether we were right in identifying those things we liked with structure within string theory- require us to understand the theory non-perturbatively. Until we have better understanding of how to compute with “string theory” (I use quotes because we know if is not just about strings, but we don’t have a better name), we don’t know for sure if it really has anything to do with Nature, and so the job is not done. That’s where research such as mine comes into the game. So I don’t write lots of papers on the sexy stuff that people apply strings to that makes it to the Press and the PBS documentaries, ‘cos I’m down in the basement and the foundations trying to understand exactly what it is we’re playing with, and what it really means and what we can and can’t do with it. Every now and again I (or people who work on this fundamental stuff) send something upstairs for the clever folks to do the sexy stuff with. It’s a thankless task, but someone’s got to do it.

    Cheers,

    -cvj

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Jack: Well, I’m safe then. I’m not a famous physicist so I’ll be left alone….Yay.

    -cvj

  • Moshe

    I like the basement picture, though I would add that it is a very nice basement, equipped with all the latest high-tech entertainment gadgets for the discerning mathematical physicist….

  • http://iso42.blogspot.com Wolfgang

    By the way, Lubos discussed non-critical strings here:
    http://motls.blogspot.com/2005/04/critical-dimension-anything-goes.html
    Eva Silverstein wrote a reply in the comment section.

    But with non-critical strings and matrix models there is the even greater danger
    that you may encounter dynamical triangulation and perhaps even LQG.
    Now I know why you waited until Halloween with your post …

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Pyracantha– I also discussed perturbation theory a little bit in my post on replacing dark matter.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Wolfgang: – I’m still not seeing the scary part here. What is wrong with making contact with other interesting physics?

    -cvj

  • Moshe

    Clifford, Lubos had an exchange with Eva on his blog a while back in which he was critical of her work on super-critical strings, raising the issue of calculational control over these backgrounds. This is different from the non-critical strings you are discussing.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Yeah, I know it’s different. Thanks. This is subcritical….. but in any case, I assume that Wolfgang was joking….making contact with interesting physics is a good thing, irrespective of who one might have to argue with.

    So how about we talk about physics now, folks? I’ve not too much interest in discussing the existence of other discussions on other physics on other blogs.

    Cheers,

    -cvj

  • http://iso42.blogspot.com Wolfgang

    > I’ve not too much interest in discussing the existence of other discussions on other physics on other blogs.

    Sure. Well, you will have to deal with (or explain away) the anomalies and the way I see it, the case for super-symmetry is mostly gone.
    It is a different story, of course, if you consider non-critical strings as toy models only.

    I wish you good luck of course.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    I beleive we’re not talking about the same thing. There are no anomalies.

    -cvj

  • http://iso42.blogspot.com Wolfgang

    > I beleive we’re not talking about the same thing. There are no anomalies.

    I assume that I am just too stupid to understand what your are talking about.
    The little I know is that cancellation of anomalies requires D=10 for superstrings
    (and D=11 for M-theory).
    In non-critical string theories one can construct some clever ways to cancel the anomalies with higher order corrections a la Eva Silverstein and I think Jaume Gouis found another construction.
    But these methods appear unphysical (see Lubos’ comments).

    But I amy have completely misunderstood your post, especially the part
    > What people never tell you is that it is a complete overstatement to say that
    > string theory can only live in 10 dimensions. This is just wrong.

  • http://iso42.blogspot.com Wolfgang

    I am even too stupid to use a keyboard:
    Gouis = Gomis and amy = may in my previous post.

  • Anonymous

    Wolfgang, the important thing is that the CFT have the right central charge. There are plenty of CFTs around that can do this, aside from the usual flat target space with constant dilaton. A well-known example is the linear dilaton.

    If you’re looking at old blog posts, you should see one by Jacques Distler, http://golem.ph.utexas.edu/~distler/blog/archives/000551.html.

    The low-dimensional noncritical string theories are not controversial in the way the supercritical ones are. Give Clifford some credit.

  • http://iso42.blogspot.com Wolfgang

    Anonymous,

    Jacques points out what the problem is with super-critical models using a linear dilatons in the post you link to:
    “However, for supercritical strings, the theory is strongly-coupled either in the far future or in the far past. It’s not clear how one defines an S-matrix.”

    Again, at this point I assume that I have completely misunderstood what Clifford
    is doing, since he certainly knows all this much better than I do (by a factor of many gogols 8-) .

  • Anonymous

    Wolfgang, note that Jacques also mentions the 2-d subcritical string:

    “In 1+1 dimensional noncritical string theory, there is also a linear dilaton background (varying in a spacelike direction). And there’s a “Tachyon wall,” preventing strings from penetrating the region of strong coupling. So one has an S-matrix, of sorts, for string coming in from the weakly-coupled region, bouncing off the wall, and returning to the weakly-coupled region.”

    See? In that case you do have some notion of an S-matrix.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Anonymous…. you’ve answered all the points for me. Thanks. That was very helpful. I have not read any of the discussion of the stuff on those other blogs, and so could not comment on their content.

    I was busy with other things, not ignoring you Wolfgang. I did not mean my short reply to be a slap in the face, which is how you seem to have taken it….It’s just that I have this job I get paid for and it takes me away from blogging from time to time so my answers are not always as immediate, long (or existent) as at other times!

    Cheers!

    -cvj

  • http://iso42.blogspot.com Wolfgang

    Anonymous,

    Jacques wrote a nice post about the subcritical model you mention,
    several years ago
    http://golem.ph.utexas.edu/~distler/blog/archives/000206.html

    Interesting indeed, but can we agree that this falls in the category of “toy model” ?

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  • http://www.pyracantha.com Pyracantha

    Clifford:

    Sorry to say this, but you lost me after the first paragraph. I will print your reply out and save it until I am able to understand it, which may be a few years from now. I have not studied pendulum motion yet. I am still trying to fathom F=ma and sliding blocks, let alone Newton’s law of universal gravity. I am a real slow student.

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Wolfgang: “toy model”…. ah yes, I was waiting for that polite euphemism people use to pour scorn on a piece of physics because it suffers from the affliction of being a tractable problem. We’re only supposed to care about the stuff we can’t make any progress in, I suppose. Well, fine. But I will remind you that the harmonic oscillator, the Ising model, the hydrogen atom, and a host of other “toy models” form the foundation of what we really know and truly understand about many diverse areas of physics.

    Cheers,

    -cvj

  • http://blogs.discovermagazine.com/cosmicvariance/clifford/ Clifford

    Pyracantha….that’s ok. Don’t fall into the common trap that people do in thinking that if they do not get it really quickly then it is either hard, confusing, or not well explained. This is a lot of the origin of people not “getting” science. They don’t realise that you have to work at it a bit. Things that are worth understanding often take time to digest. I did not intend for you to understand the pendulum -or nonperturbative string theory- all in one go if you’ve never studied it before. Take what I said (which was a bit rough and ready, admittedly) and put it alongside a proper book on the subject.

    Take the time….it is worth it.

    Cheers,

    -cvj

  • http://iso42.blogspot.com Wolfgang

    Clifford,

    the hydrogen atom is certainly not a “toy model”. The other examples you mention are important as long as they neglect the “minor details” only.
    But feel free to call you model(s) whatever you like. They are certainly very important, otherwise you would not analyze them.

  • http://eskesthai.blogspot.com/2005/09/cft-and-tomato-soup-can.html Plato

    Well, I like the reference to the simple experiments of the pendulum, but this can be taken further?

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