Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-07-20
Int.J.Mod.Phys.A18:5541-5612,2003
Physics
High Energy Physics
High Energy Physics - Theory
81 pages LaTeX, 8 eps figures
Scientific paper
10.1142/S0217751X03016136
We present a universal normal algebra suitable for constructing and classifying Calabi-Yau spaces in arbitrary dimensions. This algebraic approach includes natural extensions of reflexive weight vectors to higher dimensions, related to Batyrev's reflexive polyhedra, and their n-ary combinations. It also includes a `dual' construction based on the Diophantine decomposition of invariant monomials, which provides explicit recurrence formulae for the numbers of Calabi-Yau spaces in arbitrary dimensions with Weierstrass, K3, etc., fibrations. Our approach also yields simple algebraic relations between chains of Calabi-Yau spaces in different dimensions, and concrete visualizations of their singularities related to Cartan-Lie algebras. This Universal Calabi-Yau Algebra is a powerful tool for decyphering the Calabi-Yau genome in all dimensions.
Anselmo Franco
Ellis John
Nanopoulos Dimitri V.
Volkov Gennady
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