Three String Theory Textbooks

Until very recently, someone who wanted to begin studying string theory seriously had really only three possible textbooks available:

  • Superstring Theory (1987), by Green, Schwarz and Witten. This is a two-volume, massive 1000 page treatment of the quantization of the superstring and ideas about Calabi-Yau compactifications dating from right after the First Superstring Revolution in 1984.
  • String Theory (1998), by Polchinski. In two volumes and 900 pages this covers most of what is in Green-Schwarz-Witten, while also surveying D-branes, the second Superstring Revolution, and much of what was learned about string theory during the decade after GSW.
  • A First Course in String Theory (2004), by Zwiebach. This is the textbook for an undergraduate course, so is at a lower level than the other two books.

Very recently three new string theory textbooks have appeared, each aimed at providing a textbook for an advanced one-year graduate course, assuming a background in quantum field theory and the standard model. Each of them is quite a bit shorter, while trying to cover much more than Polchinski and GSW. This is a daunting task. Polchinski in his introduction noted how difficult it was to cover even in 900 pages a literature of size around 10,000 papers. These new books are trying to cover a literature probably twice as large in sometimes half as much space. As a result all three of them necessarily often have a rather telegraphic feel, more that of a review article than the usual sort of introductory textbook.

I’ve spent some time reading through all three books over the last couple months, and here are some impressions. Just as these books are too short to really cover the subject, my comments here will be much too short to do justice to the 1800 pages or so of material in the books.

Michael Dine’s Supersymmetry and String Theory actually probably shouldn’t be thought of as a string theory textbook (and on page 310 the author notes “This is not a string theory textbook”). The first 300 pages have nothing to do with string theory, instead consisting of an introduction to the Standard Model, beyond Standard Model Physics (especially supersymmetry), and cosmology. The last 175 pages of the book give a very sketchy survey of string theory, concentrating on prospects for getting unification and particle physics out of it. Dine starts out with the standard promotional material for this idea, but does clearly explain the fundamental problems such as that of moduli stabilization that have led to the landscape and the ever-more-clear failure of this idea. He ends with a chapter about this and about the anthropic landscape. The main concern of most string theorists over the past 10 years, AdS/CFT duality, gets just two pages. For other reviews of the book, see one by Jacques Distler, and one by Lubos Motl (whose endorsement of the book’s contents as “state-of-the-art picture of reality” appears on the book’s cover). One peculiarity is that when he turns to general relativity and string theory, Dine switches his convention for the sign of the metric. Perhaps the book is best thought of as mostly an introduction to supersymmetry in particle physics, with the string theory material an outgrowth of that central topic.


String Theory in a Nutshell
, by Elias Kiritsis, is one of what I guess Princeton University Press intends to be part of an “in a Nutshell” series, beginning with Tony Zee’s Quantum Field Theory in a Nutshell. Zee’s is a wonderful book, although it’s best for someone who has already taken a QFT course and wants to get further insight into the theory, or read as a supplement to a more detailed text like Peskin and Schroeder. The Kiritsis book is not much longer than Zee’s (they are both somewhat less than 600 pages), but is much more intended as a standalone textbook for a one-year string theory course, replacing Polchinski. It contains a wealth of exercises, nearly 500 of them (and the author warns that some are hard enough to have been the subject of research articles). While the book begins with the standard promotional pitch, Kiritsis does acknowledge that it may turn out that the subject is “an intellectual classical black hole”. He pretty much completely ignores the moduli stabilization problem and the landscape. AdS/CFT gets a long chapter of about 70 pages, with 62 exercises. I don’t know of any other reviews yet, but Lubos Motl’s endorsement (which doesn’t appear on the cover) can be found in Princeton University Press’s promotional material for the book.

The most complete of the three books is String Theory and M-theory, by John Schwarz and the Becker sisters. It is more than 700 pages long and is intended as the textbook for a year-long graduate course, taking students from the basics of string theory to the latest ideas about flux compactifications and moduli stabilization. Trying to cover such a huge subject in this space means that it is done in much the “in a nutshell” style of Zee’s QFT text. As a result many sections of the book have more the feel of a review article for a general audience than that of a textbook for students. The calculations leading to the landscape are covered in some detail, and there’s a discussion of anthropic arguments and statistical calculations. Like Kiritsis, a 70 or so page discussion of gauge-string duality is provided. There’s a review by Capitalist Imperialist Pig, and a short mention from Lubos Motl. No endorsement from Lubos on the book, instead it carries endorsements from the leading figures of the subject (Arkani-Hamed, Gross, Strominger, Vafa and Witten).

I found all three books quite interesting to spend some time going through, as they each in their own way provided an overview of the current state of string theory as a unified theory of particle physics. Of the three, Becker-Becker-Schwarz I think gives the most complete coverage of where the subject is at. Dine is a separate case, since it’s mostly about other things. As you might guess I’m highly dubious of the idea of teaching this sort of material in a standard class for graduate students. The fundamental problem is that the very speculative idea that these books are devoted to, that you can unify particle physics using 10/11 dimensional string/M-theory together with compactification and branes in order to make the extra dimensions invisible, is one that has by now pretty clearly failed. Dine comes the closest to explaining how problematic the situation is, Kiritsis is at the other end, choosing to not explain the nature of the problems. These books attempt to cover a huge literature which consists of failed attempts to make some sort of connection with the real world, and I can’t think of any other field of physics or mathematics where there are graduate-level textbooks that could be characterized in this way. Unfortunately, much of what has been successful about string theory is ignored in these books. Mirror symmetry, which has had a huge effect on mathematics, is not even mentioned by Dine, gets a couple pages in both Kiritsis and Becker-Becker-Schwarz. While ignoring string theory’s mathematically most interesting insights, these books lead students into a horrendously complicated thicket of speculative ideas that generally don’t work, but provide enough grist for decades of research projects to come. Any student who chooses to follow this path will need to devote many years to mastering this material, a one-year graduate course is not going to do the trick. There’s no particular reason to believe that this kind of training is one that will lead to a solid background in techniques that are likely to have more success in the future.

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20 Responses to Three String Theory Textbooks

  1. King Ray says:

    Hmmm… The latest edition of Ptolemy’s Almagest is 693 pages. It seems that these overly baroque theories need longer texts to explain them. You would hope that the ultimate theory would be explainable in 10’s of pages.

  2. baroque says:

    “You would hope that the ultimate theory would be explainable in 10’s of pages.”

    I would? Are you aware of any reasonable treatment of any nontrivial aspect of physics which can be explained coherently in 10 pages?

  3. Peter Woit says:

    baroque,

    These books aren’t like Peskin and Schroeder, explaining in detail how to do calculations that can successfully be compared to experiment. Mostly they’re quite sketchy. Dine does the Standard Model in under 20 pages, and all of cosmology in 9 pages.

    But, the problem with these string theory textbooks is not their length. Peskin and Schroeder is 800 pages long, but it explains in detail how to do a wide range of calculations that can be successfully compared to experiment. Nothing in any of the thousands of pages in these books allows you to compute anything that can be compared to experiment. The Almagest is definitely better on that score.

  4. King Ray says:

    baroque, if you can’t explain your theory in 10’s of pages, I think you’re on the wrong track, as is becoming slowly apparent to almost all on the string theory front.

    Look at Einstein’s The Meaning of Relativity, Landau and Lifschitz’s Mechanics, etc. for some beautifully simple expositions.

    Beauty and Simplicity should be the key characteristics of the ultimate theory.

  5. Arun says:

    “The latest edition of Ptolemy’s Almagest is 693 pages. It seems that these overly baroque theories need longer texts to explain them.”

    De Revolutionibus is 330 pages as per Wikipedia.

  6. ali says:

    Hi peter,
    What do you think of the princeton university’s latest press release?
    http://www.physorg.com/news97339219.html
    Thanks

  7. Peter Orland says:

    Some years ago, I remember that Princeton supposedly dropped
    their field-theory course and taught string theory instead. I presume this has since been recognized as a mistake, but I don’t know for certain.

  8. marketing says:

    I’d argue differently. If anybody is considering writing a book on these topics, they better make sure it comes out in the market right now. Two years from now will most likely be too late to try and sell this stuff. Whatever the LHC might bring, the name of the game will be phenomenology.

  9. Peter Orland says:

    Ali,

    This is interesting stuff, but the article fails to mention that the
    gauge theory which is (probably) equivalent to the string theory
    is N=4 Yang-Mills. This is very different (even qualitatively) from QCD, the gauge theory of the strong interactions.

  10. King Ray says:

    I think this is the paper of Klebanov’s in question:

    http://arxiv.org/abs/hep-th/0611135

    I think that all the overhyping and distorting of results for press attention is hurting string theory, since they can’t deliver on their hype. I’m sure some interesting math is going on in AdS/CFT, but it may not be related to the real world.

  11. Aaron Bergman says:

    Some years ago, I remember that Princeton supposedly dropped
    their field-theory course and taught string theory instead.

    I doubt that. Both classes were certainly taught when I was there.

  12. Peter Orland says:

    Aaron,

    This was a long time ago. I heard about it around 1987

  13. Jack says:

    http://discovermagazine.com/2007/feb/cover

    I’m not sure I understand this, but from what I’m reading it sounds like parts of string theory was experimentally verified/tested. Is this so?

  14. Peter Orland says:

    Jack,

    That is not how RHIC experiments should be interpreted. What they
    study is high-energy nuclear collisions, with goal being a plasma of
    quarks and gluons. There is no test of fundamental string theory
    (of gravity and matter) here.

    Here is what is going on. The formalism of string theory is used by some theorists to try to describe QCD, the theory of these quarks and gluons. The problem is that it really only describes what is called the strong-coupling approximation. Such approximations are not new – since 1974, there has been the lattice strong-coupling expansion, which is a non-computer-based calculational scheme. Such approximations gave us the first hints that QCD might really confine quarks.

    Unfortunately the strong-coupling approximation is not necessarily
    a good approximation. The old-time lattice people abandoned it
    in favor of numerical methods. There are unphysical aspects of
    this sort of approximation (lattice artifacts, or unphysical particles
    from the string).

    Now people are claiming that the stringy strong-coupling methods
    are a good way to study QCD, and to understand RHIC physics. But
    the real problem with any strong-coupling approach is that you can’t
    renormalize the theory – that is remove the ultraviolet cut-off. For
    this reason, I think such approximations are highly questionable.

    I go to a lot of talks on this stuff, and I always raise this issue. None of the speakers have addressed it, at least not to my satisfaction.

  15. J says:

    What do you think of the 3 early books? Any comments?

  16. valon says:

    Peter,

    In your review of the String books you wrote:
    ” Mirror symmetry, which has had a huge effect on mathematics, is not even mentioned by Dine, gets a couple pages in both Kiritsis and Becker-Becker-Dine.”
    Did you perhaps mean BBS?

    Regards.

  17. woit says:

    valon,

    Fixed

    J.,

    I haven’t looked at the earlier books closely recently, so don’t want to say much. In general, I think they are much less sketchy, actually work through a lot more of the details of how you quantize a string, which is an interesting thing to do. From what I remember GSW also has much more details about Kahler geometry, which could be useful. But I should look at the books again before making more comments.

  18. anon. says:

    How about other books dealing with string theory in slightly a less spiritual, and more practical, way? For example, check out the Red String Book: The Power of Protection (Technology for the Soul) by Berg, http://www.amazon.com/Red-String-Book-Protection-Technology/dp/1571892486

    If you’d take a more holistic approach to string, instead of blindly Popperian one you take, you’d see it differently. The people who complain that religions are wrong or ‘not even wrong’, ignore the great success of religion as a cultural, groupthink activity.

  19. David says:

    Anon.
    I’m not sure if your post was tongue in cheek or not. I’ll assume not. That said, I’m reminded of Francis Crick’s remark that over the last 2000 years philosophy has been spectacularly unsuccessful at dealing with science. I’m also reminded of attending a philosophy of science conference in the late 1970’s where the discussion was about the importance of betweenness in groups of billiard balls as important for the philosophical understanding of atoms & molecules. They seemed to have missed quantum theory. Thus, while Popper may have contributed something to science, I don’t think any of us (at least at this blog) believe that the standard philosophical approach of ONLY thinking will lead to great advances. Feynman often said that no matter how beautiful the theory, if it doesn’t agree with experiment it’s wrong. The point of science is to understand nature. We can only tell how well we are doing by comparing our theories with what nature actually does. If anyone is more spiritual and less practical, it seems to me he/she is on the string side of the debate. That doesn’t mean thinking is unimportant but at some point one must compare the thinking with nature. If I misunderstood your post, sorry.
    Best,
    David

  20. theoreticalminimum says:

    I recently came across a few shared folders of ebooks on esnip, from which I found links to some of the books mentioned by Peter, from which those interested can download the books in djvu or pdf formats. I would like to merely extend those links to this post, with the hope that Peter won’t be having too many misgivings about this seeming act of “free-education-resource-for-all” débauche. They are:
    Superstring Theory (Green, Schwarz, Witten)
    Volume 1 [http://www.esnips.com/doc/db4a2a3a-79f4-4dfb-9101-839a297f0ca3/Green-M.,
    -Schwarz-J.,-Witten-E.-Superstring-theory,-vol-1
    ]
    Volume 2
    [http://www.esnips.com/doc/f904e73d-fb9c-4e06-907c-94e1a565cf4f/Green-M.,
    -Schwarz-J.,-Witten-E.-Superstring-theory,-vol-2
    ]
    String Theory Volume 1 [DJVU] , Volume 2 [DJVU] (Polchinski),

    A First Course in String Theory [DJVU] (Zwiebach),
    String Theory and M-Theory: A Modern Introduction [PDF] (Becker, Becker, Schwarz).

    Michael Dine provides lecture notes of a course he taught in 2002, which carries almost the same title (Beyond the Standard Model: Supersymmetry and String Theory) as his book. They might be worth checking out, whether or not one unfamiliar with the book would be thinking about significant overlaps with the book’s content (maybe Peter would be in a position to inform us here).

    Eh ben voilà quoi!

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