String Theory and M-Theory: A Modern Introduction

I definitely fell into an odd class of people who wanted to educate myself about string theory, yet I am not and will never be an academic physicist. What I needed was a text that introduced string theory and its mathematical underpinnings in a rigorous way, but one that was geared more for well informed, mathematically inclined amateurs, than for graduate students.

This book fit the bill very nicely. It is not a "popular" account of the field for interested non-science majors, but it is doubtlessly a good text for an undergraduate level course in string theory for physics majors. If you prefer to avoid calculus, linear algebra, geometry, and math in general, this book is not for you. For that matter, if you don't have a reasonable grasp of quantum field theory and relativity, this book is not for you.

The great strength of this work, for me, was the clear and concise explanations of the material. Although I do own both Barton Zwiebach's, "A First Course in String Theory" and Elias Kiritsis's, "String Theory in a Nutshell" only very rarely did I feel the need to consult either of those to clarify the points made by the authors in this book.

The one niggling criticism I have is that I would have preferred there be more exercises and problems throughout the book. At least for my purposes, being engaged in self-study, struggling through exercises is key to cementing the concepts in my mind. That was where I was very glad to have "String Theory in a Nutshell," as it contains close to 500 exercises, whereas this book has around 300, divided between 'exercises' (for which solutions are provided) and the more numerous 'problems' (for which they are not).

I a bit feel stingy giving this text 4-stars simply because I'd have preferred there be more exercises, but giving it 4.5 stars is not an option. Suffice it to say that I could have just as easily rounded up to five stars.

There are a number of topics omitted by the authors that have come up in subsequent study, but it shouldn't be shocking that a 700-page treatment of a fast moving field like string theory would fail to be entirely comprehensive. Those unaddressed topics (that I presently know of) are treated in more advanced texts, and thus far I don't believe that the quality or usefulness of this book suffers for any of the omissions.

If I could only recommend one of the three introductory texts on string theory that I've read, I would generally select this one. I found the discussions far more clear in this book than I did in Kiritsis's treatment of the same topics, and both books are more mathematically rigorous than Zwiebach's "A First Course in String Theory."

Armed with what I've learned from the authors, I am now in a position where I can turn to graduate level texts without succumbing to frustration at my own ignorance. "String Theory and M-Theory" provided me with the solid foundation I was hoping for; one on which I can easily build.

The instructor of the 1-semester strings grad course I am taking uses this as the textbook. This book is a good company to a course for its conciseness and fast track to superstrings. However, I don't recommend reading it for self-learning, as it skips a lot of details and subtleties. For self-learning purpose I recommend Polchinski Book 1 and then return to the chapter of this book on superstrings and beyond.

This is a nice book to have if you're trying to learn string theory. The presentation is rather straightforward. What's really nice is each chapter has several solved examples. But best of all the writing is clear and its relatively (no pun intended) easy to follow the book to the end. In my opinion, this book is accessible to anyone with a basic physics (or even math) undergraduate education. Zweibach is a great book for sure, but by design it cuts corners in an attempt to make the subject accessible to undergraduates. I don't think thats really necessary (except maybe avoiding path integrals). What I like about this book is it does not cut corners. Topics that are avoided in Zweibach are definitely discussed in here.

Good hard-cover book. Very densive content, requires complementary books like Polchinski and Barton. However it contains
almost all the topics in strings theory.

The book seems to be very well organized and although it requires some knowledge of quantum field theory and general relativity it is quite accessible. It was delivered in very good condition albeit with two minor bumps on the front hardcover, probably due to packaging and handling. However, I am quite satisfied and am looking forward to an enlightening read.

String theory has been criticized since it was first invented but not to the degree that it has now, this criticism mostly focusing on its failure to connect with observation. The criticism has increased dramatically in recent years however, and some of this has been too vituperative to be useful to those curious about string theory as a viable physical theory. But criticism, however harsh, can be healthy, since it motivates the proponents of a theory to more carefully elucidate its foundations and content. This is usually not the case when a theory is popular, as researchers are in a competitive spirit and are hesitant to share the knowledge to possible competitors. At this stage in the game however, string theorists it seems are now on the defensive, and have thus taken the time to discuss in-depth what this reviewer still believes is the most complex and beautiful theory ever constructed in mathematical physics. String theory still has a long way to go before it gains status as being a physical theory, but hopefully by the end of the next few decades one will see the appearance of charts, graphs, and numerical calculations in books on string theory, much like one finds in the most successful of all physical theories to date: relativistic quantum field theory.

Some highlights in the book that are particularly insightful include:

1. The observation that Dirichlet boundary conditions (for the open string) break Poincare invariance, but that this leads to the introduction of Dp-branes as positions of the endpoints of the open string. Poincare invariance is recovered as long as Dp-brane is space filling, i.e. has a dimension one less than the background spacetime.

2. The view that the BRST quantization of the path integral is really a conformal field theory. This is interesting in that BRST analysis is typically thought of as a procedure for quantizing constrained systems (gauge theories being predominant examples).

3. The `Myers effect'. Sometimes referred to as the `D-brane dielectric effect', it is part of an attempt to understand the physics of non-Abelian D-branes for strong fields. One of the challenges in this understanding involves the validity of the Dirac-Born-Infeld action in these kinds of circumstances, which as the authors remark is designed for situations where the background fields and world-volume gauge fields do not vary appreciably over the distances on the order of the string scale.

4. The origin of the (classical) Virasoro algebra as the freedom of choice of gauge in the reparametrization symmetry. And along these same lines, the quantization of the Virasoro algebra is defined to the normal ordering of the Virasoro generators, and their commutators give an expression consisting of the ordinary classical term plus a "quantum" correction, the famous central extension. Thus the quantum Virasoro algebra can be viewed as a "quantum deformation" of the classical Virasoro algebra, with the central parameter as being the deformation parameter. This philosophy of deformation has found generalization in what are now called `quantum groups' (even though strictly speaking they are much more complicated objects than ordinary groups).

5. The connection of the dilaton to the Euler characteristic.

6. The role of the GSO projection in insuring consistency in the state spectrum.

7. The use of (vector bundle) K-theory to classify D-brane charges. This use arises when it is realized that the conserved R-R charges cannot be identified with cohomology classes of gauge field configurations. Instead, the D-branes are classified by K-theory classes.

8. The discussion on `primitive cohomology' and its relation to de Rham cohomology and Hodge theory.

9. The role of the Born-Infeld structure in ensuring Lorentz invariance of the T-dual description. The Born-Infeld action was once viewed as a mere historical curiosity, namely as a nonlinear generalization of the Maxwell theory, with no experimental backing. That it finds such a natural place in string theory is very interesting (but still of course lacking in experimental support).

10. The derivation of a lower bound for Newton's constant from heterotic M-theory, which is close to the observed value.

11. The argument, beautifully elucidated in this book, that type IIA supergravity may be obtained from 11-dimensional supergravity by dimensional reduction.

12. The discussion on warped space-times and the gauge hierarchy. The authors cleverly motivate this subject by asking why Newtonian gravity follows an inverse-square law rather than an inverse-cube law.

13. An entire chapter is devoted to "stringy" geometry, which is a fascinating subject given that it touches so many areas of modern mathematics.

14. The discussion of the `hidden sector' and its conjectured relation to dark matter and supersymmetry breaking.

15. The author's treatment of the AdS/CFT conjecture is superb and is by far the most interesting part of the book. The dualities shown to exists between gauge theory and string theory are a possible route to a full understanding of nonperturbative quantum chromodynamics, which to this date has defied resolution.

Some major omissions or discussions that need more elaboration include:

1. The difficulties that are actually involved in quantizing the Nambu-Goto action. The authors remark that this is due to the presence of the square root, but it would have been interesting if they would have indicated just where the trouble rises explicitly when a quantization procedure is attempted with the Nambu-Goto action. In ordinary quantum field theory, the presence of the square root is interpreted as a "nonlocal" problem, but even there this issue is not usually dealt with in a manner that is very transparent.

2. A more detailed treatment of string field theory for those readers who want to compare it to what is done in second quantization in ordinary quantum field theory.

3. The role of the Beltrami differentials in the attaining of a measure for moduli space that is invariant under reparametrizations of the moduli space.

4. No in-depth discussion of characteristic classes over and above the algebra involved in their manipulation (i.e. the wedge products). An understanding of characteristic classes is crucial to understanding superstring and brane theory, but the pages of this book mislead the unsuspecting reader that there is nothing to characteristic classes except algebraic manipulation of the differential forms. But characteristic classes have a deep geometrical meaning, and obtaining insight into this meaning has been proven to be difficult for students of string theory. This book does not provide any of this insight, nor do any of the other books currently in print on string theory.

5. Is supersymmetry absolutely necessary for the incorporation of fermions into string theory? The authors seem to argue that it is, but an explicit proof is lacking.

6. The proof that `threshold bound states' are stable is omitted, disappointing the more mathematically sophisticated reader. As the authors remark, the proof involves a special type of index theory involving non-Fredholm operators, and where one must deal with a continuous spectrum. The usual index theory breaks down since one is only dealing with elliptic operators, and contributions to the index from bosons and fermions do not necessarily have to be integers.

7. The authors should have included more discussion on mirror symmetry, beautiful subject that it is.

8. Dp-branes are asserted to be useful in incorporating non-Abelian gauge symmetries in string theory, in that they appear "naturally" as confined to world volumes of multiply-coincident Dp-branes. But is this the best way to introduce these symmetries? Is there a method, other than this one and `compactification', that is just as "natural" and does not have the contrived element that the introduction of Dp-branes sometimes has?

9. The authors need to elaborate in more detail on the definition of "stable" and "unstable" D-brane.

10. The omitting of the proof that string theories are ultraviolet finite theories of quantum gravity. This is by far the most serious omission in the book. This reviewer does not know of a reference that proves this assertion, and many in the physics community have pointed to this omission as being a sign that the string theory research community has been misled by false assertions of proof.