Geometry and Physics of Branes (Series in High Energy Physics, Cosmology and Gravitation) 1st Edition by U Bruzzo (PDF)

Description

Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time. They are essential for a comprehension of the non-perturbative aspects of string theory, in particular, in connection with string dualities. From the mathematical viewpoint, branes are related to several important theories, such as homological mirror symmetry and quantum cohomology.Geometry and Physics of Branes provides an introduction to current research in some of these different areas, both in physics and mathematics. The book opens with a lucid introduction to the basic aspects of branes in string theory. Topics covered in subsequent chapters include tachyon condensation, the geometry surrounding the Gopakumar-Vafa conjecture (a duality between the SU(N) Chern-Simons theory on S3 and a IIA string theory compactified on a Calabi-Yau 3-fold), two-dimensional conformal field theory on open and unoriented surfaces, and the development of a homology theory naturally attached to the deformations of vector bundles that should be relevant to the study of homological mirror symmetry.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I bought this book when I was searching for more material on Branes in string theory and because it was so cheap I would not loose much adding it to my shelf. I have only read Part I: “An elementary introduction to branes in string theory” Well, to say the less it is not an elementary introduction at all, fortunately I had found my elementary book for D-Branes already in Richard J. Szabo book “String Theory and D-Brane Dynamics”. Having said this, this book is quite advanced it touches branes in 5 short chapters: 1-Introduction, 2-Branes in String Theory, 3-The boundary state description of D-branes, 4- The effective action of D-branes, 5-Classical D-branes from the boundary state. I read this 5 chapters which conform Part I, in just one night. It is advanced stuff for example you learn that the metric of the branes: Fundamental string, NS5-Brane and D3-Brane are all warped and the new really new stuff for me was the idea or fact that apparently the D-branes can emit a closed string state into the bulk using these so called Boundary States, something apparently Polchinski realized somewhere in 1995, very surprising but the book does not explain sufficiently and as the other reviewer said, this book is definitely not a textbook to learn the stuff, obliged to go to the literature and original papers……..that why I gave it only 4 stars.

⭐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 my web blog

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