Calabi-Yau Manifolds: A Bestiary For Physicists by T Hübsch (PDF)

Description

Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or equivalently, with trivial canonical bundle (canonical class). They are used to construct possibly realistic (super)string models and are thus being studied vigorously in the recent physics literature. In the main part of the Book, collected and reviewed are relevant results on (1) several major techniques of constructing such spaces and (2) computation of physically relevant quantities such as massless field spectra and their Yukawa interactions. Issues of (3) stringy corrections and (4) moduli space and its geometry are still in the stage of rapid and continuing development, whence there is more emphasis on open problems here. Also is included a preliminary discussion of the conjectured universal moduli space and related open problems. Finally, several detailed models and sample computations are included throughout the Book to exemplify the techniques and the general discussion.The Book also contains a Lexicon (28 pages) of 150 assorted terms, key-words and main results and theorems, well suited for a handy reference. Although cross-referenced with the main part of the Book, the Lexicon can also be used independently.The level of mathematics is guided and developed between that of the popular Physics Reports of Eguchi, Gilkey and Hanson and the book Superstrings (Vol. 2) by Green, Schwarz and Witten on one end and Principles of Algebraic Geometry of Griffiths and Harris on the other.This is the first systematic exposition in book form of the material on Calabi-Yau spaces, related mathematics and the physics application, otherwise scattered through research articles in journals and conference proceedings.

User’s Reviews

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

⭐Despite the fact that Calabi-Yau manifolds have been used in physics for almost 30 years now, this book still remains the only one written on the topic with physicists in mind. There have been books on Topology, Geometry, and Physics (some written by mathematicians, some by physicists) which give physicists a taste of the field of topology and and the field of geometry and their relation to physics. These books are similar in spirit to those books which carry the titles Mathematical Methods for Physicists and which offer a taste of various mathematical subjects such that undergraduate physics majors learn the basic ideas of several mathematical areas (without having to really understand the areas in depth). But besides these Topology, Geometry, and Physics books,so far, no other comprehensive book on Calabi-Yau Manifolds and their relation to Physics has been written. Hence, the current book remains a unique book that serious graduate students on string theory will have to study.It is well and carefully written but it requires serious advanced knowledge from mathematics and physics. Graduate students who have mastered quantum field theory and conformal field theory and have knowledge of manifolds and Lie algebras and groups will find this book very valuable. Instead of researching the literature, this book will prove time savior by supplying them all information they need.My only request to the author is that he should update it. Since the book first appeared, there have been some developments in string theory which are worth mentioning in the book. And because this is the only available book on the topic as claimed above, both the book itself and the readers will benefit greatly from such an update.

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