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Lipatov, L. N.; Vera, A. Sabio; Velizhanin, V. N.; Volkov, G. G.

Reflexive numbers and Berger graphs from Calabi–Yau spaces. (English) Zbl 1106.81061

Int. J. Mod. Phys. A 21, No. 13-14, 2953-3005 (2006).
The authors consider the Calabi-Yau manifolds important in superstring theory as a model for the compactification of extra dimensions. They follow the method of classification of such manifolds proposed by V. Batyrev [J. Algebr. Geom. 3, No. 3, 493–535 (1994; Zbl 0829.14023)] who found a correspondence between the Calabi-Yau manifolds and so-called reflexive polyhedra. The latter are found to be connected with a certain class of graphs, the Berger graphs, containing, in particular, the class of Dynkin graphs; see also G. Volkov [Int. J. Mod. Phys. A 19, No. 28, 4835–4859 (2004; Zbl 1059.14052)]. The physical meaning of the above notions is discussed. Many specific examples are considered.
Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T60 Supersymmetric field theories in quantum mechanics
83E15 Kaluza-Klein and other higher-dimensional theories
22E70 Applications of Lie groups to the sciences; explicit representations

Keywords:

Calabi-Yau manifold; Berger graphs; reflexive polyhedra

Citations:

Zbl 0829.14023; Zbl 1059.14052
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Full Text: DOI arXiv

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