Calabi-Yau Geometries: Algorithms, Databases, and Physics
arXiv:1308.0186 · doi:10.1142/S0217751X13300329
Abstract
With a bird's-eye view, we survey the landscape of Calabi-Yau threefolds, compact and non-compact, smooth and singular. Emphasis will be placed on the algorithms and databases which have been established over the years, and how they have been useful in the interaction between the physics and the mathematics, especially in string and gauge theories. A skein which runs through this review will be algorithmic and computational algebraic geometry and how, implementing its principles on powerful computers and experimenting with the vast mathematical data, new physics can be learnt. It is hoped that this inter-disciplinary glimpse will be of some use to the beginning student.
42 pages, invited review for the International Journal of Modern Physics A
References in corpus (7)
- Brane Tilings
- Brane Tilings and Their Applications
- STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology
- The Hilbert Series of Adjoint SQCD
- Exploring the Vacuum Geometry of N=1 Gauge Theories
- Calabi-Yau Manifolds with Large Volume Vacua
- Stable bundle extensions on elliptic Calabi-Yau threefolds
Cited by in corpus (8)
- Axion Cosmology
- A search for ultra-light axions using precision cosmological data
- Calabi-Yau threefolds with large h^{2, 1}
- How Well Can We Really Determine the Scale of Inflation?
- Heterotic Model Building: 16 Special Manifolds
- Patterns in Calabi-Yau Distributions
- Extremal Bundles on Calabi-Yau Threefolds
- Early Universe Cosmology, Effective Supergravity, and Invariants of Algebraic Forms