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He, Yang-Hui

Calabi-Yau geometries: algorithms, databases and physics. (English) Zbl 1277.81059

Int. J. Mod. Phys. A 28, No. 21, Article ID 1330032, 34 p. (2013).
Summary: With a bird’s-eye view, we survey the landscape of Calabi-Yau threefolds, compact and noncompact, 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 interdisciplinary glimpse will be of some use to the beginning student.

Cited in 1 Document

MSC:

81R05 Finite-dimensional groups and algebras motivated by physics and their representations
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory

Keywords:

Calabi-Yau threefolds; vector bundles; quivers; AdS/CFT; string theory; supersymmetric gauge theory; computational algebraic geometry

Software:

SageMath; STRINGVACUA; Macaulay2; GAP; SINGULAR
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\textit{Y.-H. He}, Int. J. Mod. Phys. A 28, No. 21, Article ID 1330032, 34 p. (2013; Zbl 1277.81059)
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