Back to Basics

Well, today was the first lecture of the string theory course (part 2) that I mentioned in the previous post. And I applied the “when they think you’re going to zig, you zag” principle. They have been expecting me to dive into the whole business of open strings and D-branes and so forth (the subject of the book), and I did not. Sure, that will come, and sure, we’ll explore what they mean and what they can tell us about string theory beyond perturbation theory and so on and so forth. But I want first to spend a couple of weeks on getting to the heart of the matter. They made several standard choices along the way in doing their first semester of study of string theory. What did they mean? Why did they work? Were those the only choices? What is underlying a lot of it all, and what, when stripped down to the essence, is at the core of string perturbation theory and beyond? In other words, let’s look more closely at the path integral definition (such as it is) of a string theory (slightly schematically):

[tex] Z=\int [{\cal D}g {\cal D}X] e^{-S(X,g)}\ ,[/tex]

and make sense of all the bits. (Er, for the two of you still reading, [tex]S(X,g)[/tex] is an appropriately chosen action built out of the various quantities describing a relativistic string moving in spacetime, and the full quantity [tex]Z[/tex] describes all the possible splittings and joinings the string can do quantum mechanically, and so on and so forth. The expression is all very short hand, in the language of quantum field theory, for a lot that’s going on.)

Doing path integrals over fields ([tex]X[/tex]) is familiar enough, but how do you do the integral over all world-sheet metrics [tex]g[/tex], and the sum over all world-sheet topologies (that is what encodes all the quantum splittings and joinings)? Is it really true that you can only do string theory in the famous so-called “critical” dimensions, such as 26 and 10 (er… no!), and what is going on really? (And is this really the best starting point anyway, being so wedded to world-sheets and strings at the outset?) So before rushing off to do all the fancy fashoinable stuff, we’re going to pause a bit and linger over this sort of thing. It’ll make the fashionable stuff better motivated, and they’ll be able to read more widely, and ultimately to make (I hope) wiser choices about what problems to work on, as opposed to just doing what is the flavour of the month.

I had fun unpacking the answers to some of the above for two hours, and I think they found it quite interesting as well as unexpected. A win-win. What will we do next? Strip off a lot of the baggage of string theory and cut down to the core, exploring how to do the sum over all world-sheet metrics and topologies exactly in a series of examples, and see what lovely surprises and lessons lay in store once we’ve done that.


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14 Responses to Back to Basics

  1. Tommy says:

    Sounds like a great course actually.

  2. Clifford says:

    Thanks! I hope so. I’ve no idea what direction I’ll end up going in… will partly leave it up to how the mood of the course develops, what the students’ responses are like, the wind, what I’m thinking about in my research and so forth, and, of course, the price of fish.


  3. Belizean says:

    “Is it really true that you can only do string theory in the famous so-called “critical” dimensions, such as 26 and 10 (er… no!)”

    Please forgive my ignorance, but are you saying that you can avoid dimensions 26 and 10 and still have a scale-invariant theory (i.e. one with a constant beta function)?

  4. Clifford says:

    Heh, this from a person who rapidly placed an obnoxious and oh so well-informed comment on a recent post about there having been no advances in string theory for decades. That’s too funny. 🙂

    You can cancel the conformal anomaly in any dimension. I’ve written a lot about string theories in other dimensions here before. Look in the news from the front page on the sidebar.



  5. Belizean says:

    The only recent relevant comment that I remember is a response to your question of whether string theory media coverage is “Too Little, Too Much, or Just Right”. I wrote:

    “Coverage seems about right. The major advances in ST seem to date back to the 90’s or before. What was the big new[s] of the 00’s? KKLT? The landscape?”

    If you perceived this post as “oh so well-informed” or “obnoxious” (though I don’t see why you would), I apologize.

    Anyway, I guess there must be a problem with subcritical string theory in four dimensions (getting it to work for closed strings?). Otherwise, even yokels like me working out in the provinces of physics would have heard about it. [I do wish I hadn’t missed your posts about it, though!]

  6. Clifford says:

    I guess I find the common willingness to make all encompassing negative pronouncements about other peoples fields of research by people not informed about it to be obnoxious, yes. But indeed, yours was more mild than a lot I see, but when you asked your (good but basic) question (and thanks for asking), I could not resist pointing out the irony! 🙂 .


  7. Belizean says:

    So I take it that you do not agree that “the major advances in ST seem to date back to the 90’s or before”. If it’s not too much trouble, could you please list comparable major advances of the last decade or point me to a good review article that does?


    [BTW: A colleague I asked told me that even subcritical string theory dates back to the late 90s. True?]

  8. Clifford says:


    What does “comparable” mean? I am puzzled by such a qualification, and by what metric you are using… there have been advances, both major and minor, going on in the field a lot over the last two decades. Many of us have been very excited by them. A great deal of the current research going on, in many directions, has been fueled by such advances. I’ve blogged about a lot of them a considerable amount here and elsewhere on my earlier blog, including posts in which you’ve taken part in the discussions… Hence my puzzlement over your statement that there’s been nothing going on that merits reporting to our colleagues in the wider field of physics.

    Cancelling of the conformal anomaly in arbitrary dimensions goes back to the late 80s, in fact. Please tell your colleague. Again, the irony here is that you seemed to confidently want to dismiss the work people have been doing while at the same time not being aware of basic facts about perturbative string theory. I just found that strange, at the very least, but not inconsistent with the attitude people seem to want to bring to the table whenever someone talks about research in this particular area. I’ve never understood that.



  9. Belizean says:

    The original question to which I responded was about the proper degree of press coverage. In the 80s and 90s there were advances dubbed by workers within the field as the first and second “superstring revolutions”. To the best of my knowledge, no development of the 00s seems to have generated similar levels of excitement. Hence, the reduced media coverage. [That subcritical string theory — which strikes me, an outsider, as quite exciting –dates way back to the 80s, seems to add to the perception that the “golden age” of string theory might have preceded the 00s.

    “Again, the irony here is that you seemed to confidently want to dismiss the work people have been doing…”

    I’m afraid that I really don’t see how a brief comment on press coverage is an attempt to “dismiss the work that people have been doing”. If there have been advances in the 00s as significant as conformal anomaly cancellation, the mathematics of Calabi-Yau manifolds, D-branes, dualities/M-Theory, AdS/CFT, or braneworlds, perhaps it would be useful to list them. As I mentioned in my original post, the only possibilities that I see are KKLT and the landscape (and these date back to early in the decade).

    [Also, may I timidly suggest that you might be a tad sensitive on this subject due to encounters with others, and that you are perhaps attributing motives and “attitudes” to me that do not in fact exist?]

  10. Clifford says:


    Well I am glad to see that you’re including various things that I got the impression that you did not consider listing, based on your “back to the 90’s or before” comment.

    I’m not really so interested in the media coverage issue in terms of volume. I prefer accuracy and so would rather see 75%-95% of those articles that are written never make it to print. But that’s another issue. I think that it is important to communicate to the public and our colleagues what it is we are thinking about, whether it be considered a “revolution” or not. In fact, most good science is done in the incremental chipping away at various ideas, with sometimes hundreds of people making little bits of progress here and there. There’s been a lot of that going on, and more reporting of that would be welcome, as opposed to just the stupid and tiresome “physicists find holy grail” headlines. This was one of the reason I invested a lot of time in writing about the applications of string theory to the nuclear physics and condensed matter physics experiments (see the Physics Today May 2010 issue, and several posts I’ve written here). I actually think that is potentially one of the most important things that has happened in string theory research for a long time. Possibly we will look back at this (and what may come of it – we shall see) as one of the landmarks for string theory in the 00’s, and a very important one with consequences as far-reaching as any of the landmarks from the previous decades. It is a quiet revolution (if revolution must be used as a term at all), in which so very many of the ideas and techniques we developed in the previous two decades have been sharpened into a language that many are beginning to use, usefully, in a range of other fields. It is also an “attitudinal” landmark, in that more and more people within string theory (both young and old) have stopped making a face like they’ve stepped in something when the word “applications” comes up (and realize that there is more to achieve in physics than quests for Theories of Everything – whatever that means), and more and more people from other fields have embraced a number of the ideas and techniques and approaches that they have had a mental block about (extra dimensions, gravity, and so forth). I think this will strengthen theoretical physics in general, and feed back usefully into the development of string theory too. There are various other things going on that I find remarkable and exciting too, and perhaps I’ll talk about them in due course.

    As for your last sentence. Well, I am not attributing attitudes to you. Just poking a bit of harmless fun at an irony, as pointed out in my previous comment.



  11. Giotis says:

    Clifford, BTW are there any plans for a second edition of your book on Branes? I’m planning to buy it but if there will be a new revised edition in the near futute I’ll wait.

  12. Clifford says:


    I have not done any work on a second edition. Perhaps one day, but not soon.

    Thanks. Enjoy!


  13. Belizean says:

    Thanks for reminding me about the applications to heavy ion collisions.

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