Every so often a textbook comes along that takes a very broad and very difficult subject and explains it with a marvellous clarity of exposition. Many topics and material that in the past had left you somewhat confused or even totally stymied are suddenly made crystal clear, or at the least are greatly clarified.  Such is the case with the beautiful new string theory textbook by John Schwarz and Melanie and Katrin Becker called String Theory and M-Theory–A Modern Introduction.

String theory has become much maligned in recents years with its detractors claiming that a string-theoretic construction of ‘a theory of everything’ has failed, that it is ‘not physics’ and that it cannot hope to ever connect with reality. However, most of them fail to appreciate that nature is already full of examples of fluctuating line-like or string-like objects: these include defects in crystals and liquid crystals and condensed medias, vortex lines in superfluids and turbulence, flux tubes in superconductors and qcd, polymers in solutions, biopolymers like polypetide chains/proteins and dna, and even viruses. (Path integrals are usually particularly useful tools to describe such fluctuating line-like structures like polymers.) Biology in particular, over many length scales, seems to be built from fluctuating string-like structures and membranes or ‘branes’. It is therefore still reasonable to suspect (in my opinion) that this is a hint that at the most fundamental level the building blocks of the universe might actually be string-like and brane-like structures, even if we cannot yet fully understand, develop or manipulate such a theory.

Certainly there are currently difficulties and roadblocks in string theory. But even if you believe that a string-based unification program can never work, there is no denying the fact that string theory is an astonishingly tantalizing and remarkably self-consistent and rich mathematical structure worth studying; and one that has still consistently produced many tantalizing and solid results over the past twenty years that simply cannot be discarded or ignored. Mathematical ideas from topology, geometry, group theory, general relativity, supersymmetry, conformal field theory and much more, converge together in a very unique way within string theory. So when you study string theory you immediately start to learn about, and be introduced to, all these things faster then you would if you studied them seperately. As well as making connections with deep mathematics, well-established physics ideas such as general relativity, holography, supersymmetry, quantum black hole theory and gauge theory also seem to be naturally encompassed by the theory. In my opinion all these reasons make the theory worth studying for its own sake, and some knowledge of it an essential part of a modern education in theoretical physics and mathematical physics, and even mathematics. The technical tools and mental exercise acquired in the process are also worth the effort. But it is a vast and difficult subject and up until now it has been rather difficult and somewhat overwhelming to find an entry-way into string theory. This is where the book really does a first-rate job.

The book is unique in that authors begin right at the beginning with the simple action for the bosonic string and within 700 pages clearly guide the reader to the latest developments and topics such as the ADS/CFT correspondance, black holes in string theory, M-theory, D-branes and dualities, cosmology and even the (much-maligned) flux compactifications and landscape. They present the essential technical and mathematical material in a very clear and logically progressive way but never oversimplify anything; but at the same time they do not overwhelm, confuse or drown the reader with too much technical detail either. Both the classic GSW and Polchinski Vols 1 and 2 are excellent texts but can be somewhat overwhelming to a beginner, student or someone from a different physics or math background trying to learn about the theory. Some of the sections in BB&S do have the feel of a review article but this is really what you want when first studying the topic. You can then go and read GSW or Polchinski or even the original papers for more details later. I have found that things in GSW and Polchinski that had left me puzzled or just plain stuck where understandable after working through the same material in BB&S that introduced the topic. I think all these texts now really compliment one another rather well.

A real strong point of the book from the pedagological point of view (to use an established phrase) are the many worked examples and problem sets throughout. There are about 120 worked examples throughout the text, which I found very illuminating. At the end of each chapter there are plenty of problem sets to try. My only gripe is that the solutions are only available at a password-protected site and only seem to be available to people who can prove they are actually teaching a string theory course, not for people engaged purely in private study for their own private use. I don’t think this is fair at all. I don’t mind paying the asking price for the book but feel this should also include access to the solutions for private use. If you have studied the chapter many of the problems are doable though and some are a lot of fun. Even the ones you can’t do still give you plenty to think about and are good mental exercises worth trying. Another thing about the book I like is its beautiful production: it is printed on very glossy and shiny white quality paper and the cover is a nice glossy black and orange (with a painting done by the mother of B&B). This makes the book a pleasure to use and work with and it is not at all like a dry textbook. I have been working through the book and trying the exercises in 15-20 minute sessions here and there when I have time, really just for fun, and have been surprised at how quickly you can get through the material when it is presented this clearly. (Actually, this is usually how I have studied mathematical/technical material–in short bite-sized chunks in short study sessions.)

To elaborate, the book takes the reader from the basic bosonic string (introduced very clearly and quickly with just enough detail and a minimum of fuss) and then quantizes this, studies the spectrum (which contains a graviton for closed string) then leads into conformal field theory and the elements of perturbative string theory; fermionic degrees of freedom, world-sheet supersymmetry and then spacetime supersymmetry follow, then the various superstring theories and the heterotic string; we then move into modern developments with D-branes, dualities, M-theory. Some highlights include a very nice discussion of string geometry (eg. Calibu-Yau compactifictions) which connects with much modern mathematics, and a chapter introducting black holes and the origins of BH entropy within string theory. Getting Type IIA supergravity from 11-dimensional supergravity is also nicely shown. The final chapter is on ADS/CFT and is an excellent intro to this important topic. These later chapters I have mostly skimmed through and have not reached yet or studied fully as there is a lot of material and I have limited time. The more mathematically oriented reader will probably notice a lack of in-depth discussion on things like mirror symmetry and characteristic classes and probably would like more on string field theory (which is at least included). One thing lacking is a discussion of proof of the ultraviolet finiteness of string theory as a quantum theory of gravity, which really should not be glossed over. Even two or three pages on this would have been very welcome. But as previously stated, the function of the book is to provide an entry way into what is a vast arena, at which it succeeds with full marks, and various advanced topics like these can be pursued in other texts or in the actual papers and preprints.

String theory is still a solid body of scholarship and a beautiful area of mathematical physics, and should be respected as such, even if it remains detached from experiment. Even if you don’t believe it can connect to reality–although in the end I believe some part of it at least will be found to be–you can still treat it as a ‘ gymnasium’ where you can exercise your mind and learn about a great deal of mathematics and physics in a unified way. I certainly recommend this book and feel I have learned, and am still learning, much from it.