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
