Reflexive Numbers and Berger Graphs from Calabi-Yau Spaces

Details Reflexive Numbers and Berger Graphs from Calabi-Yau Spaces Reflexive Numbers and Berger Graphs from Calabi-Yau Spaces

2005-01-14

arxiv.org/abs/hep-th/0501101v3

Int.J.Mod.Phys.A21:2953-3006,2006

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 5 figures, 5 tables. Extensively rewritten, references added

Scientific paper

10.1142/S0217751X06031326

We review the Batyrev approach to Calabi-Yau spaces based on reflexive weight vectors. The Universal CY algebra gives a possibility to construct the corresponding reflexive numbers in a recursive way. A physical interpretation of the Batyrev expression for the Calabi-Yau manifolds is presented. Important classes of these manifolds are related to the simple-laced and quasi-simple-laced numbers. We discuss the classification and recurrence relations for them in the framework of quantum field theory methods. A relation between the reflexive numbers and the so-called Berger graphs is studied. In this correspondence the role played by the generalized Coxeter labels is highlighted. Sets of positive roots are investigated in order to connect them to possible new algebraic structures stemming from the Berger matrices.

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