2 of 2 people found the following review helpful:
4.0 out of 5 stars
Not a textbook, June 22, 2006
This review is from: Geometry and Physics of Branes (Series in High Energy Physics, Cosmology and Gravitation) (Hardcover)
This book should not be considered as a textbook for either graduate or undergraduate students. Even although, as the editors explain in the preface, it brings together the contents of the courses given at the doctoral school on `Geometry and Physics of Branes' which took place in Italy in 2001. The reason for this is that this book is not a self-contained and pedagogical text on the subject. Rather, it is a concise introduction to the following current lines of research in the mathematics and physics of branes: two-dimensional conformal field theory on open and unoriented surfaces, string tachyon dynamics, mirror symmetry, and the Gopakumar-Vafa conjecture. As a consequence, one has to be familiar with fundamental concepts in both mathematical and physical aspects of string theory in order to read the book. In my viewpoint, the minimum prerequisite for the physical aspects should be Zwiebach, Polchinski vol. I and some of Polchinski vol. II, and for the mathematical aspects should be the whole of Nakahara.
The book is organized into three parts. The first part, consisting of five extremely short chapters, introduces branes in string theory and the corresponding effective action. Although this part tells little to either those who already know the material therein or to beginners in string theory, it is still better than none as it provides many of useful formulae and equations that save the readers from having to look them up somewhere else. Part 2 focuses on the physical aspects via two larger chapters--chapters 6 and 7-- contributed by Y. Stanev, C. Gómez and P. Resco. Chapter 6 addresses the topic of two-dimensional conformal field theory on open and unoriented surfaces with an emphasis on the construction of correlation functions and partition functions. Chapter 7 deals with string tachyon dynamics. Part 3, an account of the mathematical aspects of String Theory, contains Chapters 8 and 9, which are the contribution of K. Fukaya, A. Grassi and M. Rossi. Chapter 8 discusses homological algebra and deformation theory and their application to mirror symmetry. Chapter 9 explains Gopakumar-Vafa conjecture and a possible way to tackle it.
Part I and each of Chapters 6 through 9 have references to carefully selected articles closely related to their content. The definitions, theorems, lemmas, etc. are nicely phrased and thus may refresh the memories of those who already know some of them. For most of the lemmas and some of the theorems the authors provide full proofs. For the case where a full proof is not given the authors give either a sketch of proof or a reference. Unfortunately, there are very few exercises for students to work through. This provides yet another reason why the book is not as appropriate as a textbook. Small compensation is found, however, in the number of well treated examples that are presented.
Chapters 6 through 9 are independent of each other to a great extent allowing the reader to only read the chapter he or she is interested in. Nevertheless, one should not expect a full understanding of the material without reading the referred articles. On the other hand, it may not be necessary for one to read the book word by word. I would suggest reading the reference articles indicated in the book and come back to the book for hints or solutions to comprehend the difficult parts of the articles.
In summary, the goal of this book is to inspire the readers to follow in their own research one or more of the research lines being discussed. In this sense, I think it should be successful in this sense. Therefore, with my aforementioned reservations, I recommend this book to those advanced graduate students and researchers who take this subject seriously and are willing to dwell in any of the research directions described in the book.
A slightly different version of this review can be found on <a href="http://www.wanyidun.com/blog_r2u/?p=74">my web blog</a>
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