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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.
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.
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