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.
