D-Branes (Cambridge Monographs on Mathematical Physics) [Englisch] [Taschenbuch]

While it provides a (in some sense) self-contained introduction to string theory, it is no secret that this was not the intended focus of this text (as indicated even by its title), so prior knowledge of string theory would be highly beneficial. It does however provide a novel viewpoint from which it introduces string theory, and it is so far the best/only text on D-Branes, which is a subject that has become vitally entangled with string theory, so it is worth reading for anyone in the field.

Unfortunately, the deal-breaker is that there are many non-trivial errors throughout the text, which makes it difficult to be sure you understand what you think you are learning. A positive outlook comes from the fact that the author has an errata webpage where errors are being collected, so maybe there will be a future printing with most errors corrected that would deserve 4 or 5 stars.

...If you want an intoduction to string theory, sure you should start with G,S & W or Polchinski. However, D-branes are hardly covered in these texts and I found this book a great entry point for this subject. How are you going to learn about AdS/CFT, black holes, F-theory etc by sticking to those other books?

It is not an exaggeration to say that string theory is the most complicated physical theory ever constructed. But the complexity of string theory does not have its origin in the underlying physics, but rather in the type of mathematics that is used. To do research in the frontiers of string theory entails that one needs to become an expert in areas such as algebraic geometry, complex manifolds, and algebraic and differential topology. And this expertise does mean a mere formal or computational mastery of these areas, but rather deep insight into the concepts that are used in them. This insight is best obtained from speaking directly to the mathematicians who developed these concepts, but they are not always accessible to the researcher. Therefore such researchers must rely on what is in print, and the string theory literature, along with the mathematical literature that supports it, is usually not written in a way that gives the interested reader the needed insight. The latter is typically much too formal, and in the interest of mathematical rigor the intuition behind the concepts has been completely removed.

This book, which emphasizes the research in string theory that has been done in the last decade (the so-called "second superstring revolution"), is one that is of assistance in granting this insight. The author discusses the theory of D-branes, which loosely speaking is a high-dimensional generalization of string theory. The theory of D-branes though was not invented out of sheer fancy, but rather to resolve certain issues in ordinary string theory. Ordinary string theory was invented because of the difficulties in deriving a workable theory of quantum gravity from quantum field theory. That string theory gives a successful theory of quantum gravity is currently hotly debated, but the author of this book believes that it has, at least in what is ubiquitously called the `perturbative regime.' But just as in ordinary quantum field theory, where the performing of calculations involving particles that subjected to strong interactions is difficult, so is the understanding of strongly coupled strings.

The theory of D-branes tackles the issue of strong coupling by bringing in the concept of `duality.' Loosely speaking, duality is a kind of transformation that operates on a strongly coupled theory of strings and gives a weakly coupled theory. The author introduces duality by studying the spectrum of strings that are propagating in a spacetime with a compact direction. Readers who have done calculations in quantum field theory in Kaluza-Klein spacetimes will find somewhat familiar territory here. There is an interesting difference in the case of strings however in relation to the compact dimension. As the author points out, closed strings can wrap around the compact direction, the net result being that the spectrum of states will contain some with mass proportional to the radius. Therefore if the radius decreases, these states, called `pure winding states' will become lighter. Further, they form a continuum as the radius decreases to zero, leading to the reappearance effectively of the uncompactified dimension. The mathematical formula for the spectrum also has the property that it is invariant under the interchange of the radius with its inverse, implying that a string that propagates on a large circle can be related to a string that propagates on a small circle. This is the famous `T-duality' that is widely discussed in the literature. When one considers the case of open strings, where attention must be paid to the boundary conditions, the T-duality transformation interchanges Neumann and Dirichlet boundary conditions. The ends of the string lie on special hypersurfaces called D-branes, which are of course the main focus of this book.

So what do D-branes do for a theory of elementary particle interactions? Why should an inspiring researcher in elementary particle physics choose to study their properties? The author's treatment of these properties in the book reveals many reasons why D-branes are important. One has to do with the possibility of discovering a new conception of spacetime than what was available in quantum field theory. Another reason was mentioned above: D-branes allow one to probe the non-perturbative regime, which has traditionally been very difficult to deal with. Also, D-branes are "localized" solutions to string theory, and provide backgrounds in which strings can propagate. In addition, the low-energy dynamics of D-branes can be related to ordinary gauge theory, in that the spacetime in which the D-branes move can be interpreted with reference to the vacuum expectation values of scalars in a world-volume gauge theory.

Further, D-branes can be used to study M-theory, the latter being the formulation of string theory that caused so much excitement among theorists. M-theory related the five different string theories to each other using duality transformations, but it is still unclear as to the true nature of M-theory. There have been several proposals for studying M-theory, going by the names `matrix theory' and `F-theory.' The author studies these approaches and how D-branes are used in them in the book. The reader will note that the mathematics begins to get very esoteric in these discussions, particularly in the use of algebraic geometry in the examining the properties of the type IIB string in terms of F-theory.

Since D-branes shed light on the non-perturbative properties of string theory, and the latter is viewed as a theory of quantum gravity, it would be natural to assume that D-branes could be used to understand the physics of black holes. The author spends a good portion of the book in discussing just how effective D-branes are in accomplishing this. He shows that one can construct a black hole out of the geometry of D-branes for D = 5, and derives the metric for this geometry. Even more interesting (and controversial) is that he claims when doing this that he has found a microscopic description of black holes. These properties of D-branes motivate him to consider in more detail the consequences of duality, which he does by showing a duality between large N gauge field theory and gravity.