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arXiv · hep-th/0307244

Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case

M. Ait Ben Haddou·A. Belhaj·E. H. Saidi
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Abstract

Using Katz, Klemm and Vafa geometric engineering method of $\mathcal{N}=2$ supersymmetric QFT$_{4}$s and results on the classification of generalized Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of $\mathcal{N}=2$ CFT$_{4}$s based on \textit{indefinite} singularities. We show that the vanishing condition for the general expression of holomorphic beta function of $\mathcal{N}=2$ quiver gauge QFT$_{4}$s coincides exactly with the fundamental classification theorem of KM algebras. Explicit solutions are derived for mirror geometries of CY threefolds with \textit{% hyperbolic} singularities.

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M. Ait Ben Haddou, A. Belhaj, E. H. Saidi. 2003-11-25. Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case. https://doi.org/10.1016/j.nuclphysb.2003.08.037

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