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Calabi–Yau spaces are complex spaces with a vanishing first Chern class, or, equivalently, with a trivial canonical bundle (sheaf), so they admit a Ricci-flat Kähler metric that satisfies the vacuum Einstein equations. Used to construct possibly realistic (super)string models, they are being studied vigorously by physicists and mathematicians alike. Calabi–Yau spaces have also turned up in computations of probability amplitudes in quantum field theory. This book collects and reviews relevant results on several major techniques of (1) constructing such spaces and (2) computing physically relevant quantities such as spectra of massless fields and their Yukawa interactions. These are amended by (3) stringy corrections and (4) results about the moduli space and its geometry, including a preliminary discussion of the still conjectural universal deformation space. It also contains a lexicon of assorted terms and important results and theorems, which can be used independently.
The first edition of Calabi–Yau Manifolds: A Bestiary for Physicists was the first systematic book covering Calabi–Yau spaces, related mathematics, and their application in physics. Thirty years on, this new edition explores the intense development in the field since 1992, providing an additional 400 references. It also addresses advances in machine learning and other computer-aided methods that have recently made physically relevant computations feasible, opened new avenues in the field, and begun to deliver concretely on the now 40-year-old promise of string theory. The presentation of ideas, results, and computational methods is complemented by detailed models and sample computations throughout. This second edition also contains a new closing section, outlining the staggering advances of the past three decades and providing suggestions for future reading.
Sample Chapter(s)
Preface, 2024 Edition and 1992 Edition
Chapter 0: Spiritus Movens
Contents:
- Preface, 2024 Edition
- Preface, 1992 Edition
- About the Author
- Spiritus Movens
- Constructions:
- Complex Kindergarten
- Complete Intersections in Products of Projective Spaces
- Some More General Embeddings
- Group Actions, Quotients and Singularities
- Embeddings in Weighted Projective Spaces
- Fibered Products
- Cohomology:
- (Co)homology Basics
- Topological Triple Couplings
- (Co)homological Algebra
- Tangent Bundle Valued Cohomology
- Other Tangent Bundle Related Cohomology
- The (2, 1) Triple Couplings and Generalization
- Changelings:
- Parameter Spaces: From Afar
- Parameter Spaces: A Closer Look
- Concordance:
- A Prelude to Quantum Geometry
- Lexicon
- Afterword
- Bibliography
- Index
Readership: This book is suitable for physics and mathematics graduate and advanced undergraduate students, postdocs and faculty, as well as active researchers in the fields of string theory and algebraic geometry.
